Class 8 Maths - Comparing Quantities

Calculate $$85$$% of 9.

To find:

85 % of 9

$$=\dfrac {85}{100} \times 9$$

$$= 0.85 \times9$$

$$= 7.65 $$

Calculate $$10.25$$% of $$120$$.

We need to find $$10.25\%$$ of $$120$$

Let that be equal to $$x$$

Now it is equal to $$\dfrac {10.25}{100}\times 120=x$$

$$\Rightarrow x=12.3$$

A dealer sells goods priced at Rs 180 after giving a discount of 25%. Find his selling price (in Rs).

Selling price after discount = $$\displaystyle 180\left ( 1-\frac{25}{100} \right )=135$$

Calculate $$16$$% of $$1400$$

To find: $$16$$ $$\%$$ of $$1400$$

$$= \dfrac {16}{100} \times 1400$$

$$= 0.16 \times 1400$$

$$= 224 $$

What is 12 % of 90 ?

To find; $$12 \% of 90$$

$$\Rightarrow\dfrac {12}{100} \times 90$$

$$\Rightarrow 0.12 \times90$$

$$\Rightarrow 10.8 $$

Calculate $$10.5$$ % of 100.

To find: $$10.5 \% of 100$$

$$\Rightarrow\dfrac {10.5}{100} \times 100$$

$$\Rightarrow 0.105 \times 100$$

$$\Rightarrow 10.5 $$

What is $$45$$% of 80?

To find: $$45 \% of 80 $$

$$=\dfrac {45}{100} \times 80$$

$$= 0.45 \times 80$$

$$= 36 $$

Define discount percentage with respect to marked price.

Discount is defined as the amount of rebate given on the label price (marked price) of an article.

It is given by merchants/shopkeepers for attracting customers for increasing their sales.

Discount percentage $$= \left[\dfrac{\left(Discount\right)}{\left(Marked \ price\right)}\right]× 100$$.

A dress is sold at $$Rs. 550$$ after allowing a discount of $$12$$%. Find its marked price

Given, Rate of discount $$= 12$$%

Let the marked price be $$Rs. x$$.

Then,

$$ S.P. = x - 12\% \ of \ x \\= x-\dfrac{12}{100}x \\=x-0.12x=0.88x$$

Given, $$ S.P. = Rs. 550$$

$$0.88 x = 550$$

$$x=\dfrac{100 \times 550}{88} \\ \ = \dfrac{55000}{88} = 625$$

Marked price $$ = Rs. 625$$.

Arun bought a pair of skates at a sale where the discount given was $$20$$%. If the amount he pays is $$Rs.\ 1,600$$, find the marked price.

Discount $$= 20\%$$

Selling price of the skates $$=$$ Rs $$1600$$

Marked price $$=\dfrac { 100 }{ 80 }\times1600 =$$ Rs $$2000$$

Marked price $$=$$ Rs $$2000$$

Before beginning her diet, Janet weighed $$125$$ pounds. After completing the diet, she weighed $$110$$ pounds. What percent of her weight did she lose?

The weight she lost during diet is $$125-110 = 15$$ pounds

The percent of weight she lost is $$\frac{15}{125} \times 100 = 12$$%

What percent of 20 is 30?

Let $$x\%$$ of $$20$$ be $$30$$.

Hence, $$ x\% \ of\ 20 = 30$$

In math, 'of' means multiply.

Hence, on replacing 'of' with multiply, we get:

$$\therefore\ x\% \times 20 = 30 $$

$$\Rightarrow \ \dfrac{x}{100} \times 20 = 30 $$

$$\Rightarrow x = \dfrac{30}{20} \times 100$$

$$\Rightarrow x = \dfrac {3}{2}\times 100 $$

$$=150\%$$

Hence, $$30$$ is $$150\%$$ of $$20$$.

During a sale, a shop offered a discount of $$10$$% on the marked prices of all the items. What would a customer have to pay for one jeans marked at $$Rs. 1450$$ and two shirts marked at $$Rs. 850$$ each?

Discount on the jeans $$= 10\%$$ of Rs $$1450$$ =$$1450\times\dfrac{10}{100}$$$$= Rs $$$$145$$

Costs of both the shirts $$=$$ Rs $$850 + 850 = 1700$$

Discount on the the two shirts $$= 10\%$$ of Rs $$1700$$ =$$1700\times\dfrac{10}{100}$$$$ Rs$$ $$170$$

Total discount $$=$$ Rs $$145 + 170 =$$ Rs $$315$$

Selling of the goods $$= (1450 + 1700) - 315 =$$ Rs $$3150 - 315 =$$ Rs $$2835$$

A person pays $$2,800$$ for a cooler listed at $$3,500$$. Find the discount percent offered.

Discount offered$$=\cfrac{3500-2800}{2800}\times 100=20\%$$

Hence $$20\%$$ discount offered.

Find the discount when the marked price is Rs.$$25$$ and the selling price is Rs.$$23$$.

Given, Selling Price$$=Rs. 23$$ and Marked Price$$=25$$
Selling Price$$=$$Marked Price$$-$$Discount
$$\therefore$$ Discount$$=$$Marked Price$$-$$Selling Price
$$=Rs. 25- Rs. 23$$
$$Rs. 2$$
Thus, discount is $$Rs. 2$$.

Find: $$0.6\ \%\ of\ 45=\dfrac{m}{100}$$. Find $$m$$

$$\dfrac {6}{10}$$ % of 45 =$$\left (\dfrac {6}{10}÷100\right) ×45$$

$$=\dfrac {\dfrac {6}{10}×45}{100}$$

$$=\dfrac {27}{100}$$

Find $$32 \%\ of\ 425$$

Solution:-

$$32 \% \text{ of } 425 = \cfrac{32}{100} \times 425 = 8 \times 17 = 136$$

Hence, $$32 \% \text{ of } 425$$ is $$136.$$

Ankit bought a pair of shoes at a discount of $$30\%$$. If he paid Rs. $$1,250$$, find the marked price.

Let the marked price be $$x$$

Now,$$SP = (100 - discount)\% \times MP$$

$$\Rightarrow SP = (100 - 30)\% \times MP$$

$$\Rightarrow 1250 = 70\% \times MP$$

$$\Rightarrow MP = 1250 \times \dfrac{{100}}{{70}} = 1785.71$$rupees

Find the gain or loss:
C.P. $$=$$Rs. $$3.50$$; S.P. $$=$$Rs. $$4.25$$.

Here, Cost price $$=Rs.\ 3.50$$

and Selling Price $$= Rs.\ 4.25$$

Since, $$S.P > C.P.$$

There is a gain.

Now, Gain$$= S.P. - C.P. = Rs.(4.25 - 3.50)=Rs.\ 0.75$$

Hence, the gain is $$Rs.\ 0.75 $$

Find the gain or loss.
C.P. $$=$$Rs. $$112.25$$; S.P. $$=$$Rs. $$131.00$$.

now, S.P. - C.P. = (131.00 - 112.25)Rs.

$$ S.P - C.P. = 18.75> 0.$$

$$ \therefore S.P. - C.P. > 0 $$

$$ \therefore S.P. > C.P.$$

So, From CP & SP, We gain.

1180640_1069014_ans_3178c969912c4384afe935f879756864.jpg

The cost of a pair of roller skates at a shop was Rs.The sales tax charged was 5%. Find the bill amount.

On Rs. 100, the tax paid was Rs. 5.

On Rs. 450, the tax paid would be = $$Rs. \dfrac{5}{100}\times 450 = Rs. 22.5$$

Bill amount = Cost of item + Sales tax = $$Rs. 450+Rs. 22.5 = Rs. 472.5$$

Find the discount and the amount paid annually if a shirt having a price tag of $$600$$ is $$15$$% discount.

Given, $$MP=600$$

$$Discount=15\%=\dfrac{15}{100}\times 600=15\times 6=90$$

Amount paid$$=600-90=510\ Rs$$

Krishnamurti bought oranges at $$Rs. 5$$ a dozen. He had to sell them at a loss of $$4%$$. Find the selling price of each orange.

Cost of $$12$$ oranges $$=$$ Rs. $$5$$

Loss after selling $$12$$ oranges $$=$$ Rs. $$4$$

C.P $$-$$ S.P $$=$$ Loss

Rs $$(5-S.P)=$$Rs. $$4$$

S.P $$=$$ Rs. $$1$$

$$\therefore$$ selling price of $$12$$ oranges $$=$$ Rs. $$1$$

Selling price of $$1$$ orange $$=$$ Rs. $$\dfrac{1}{12}$$ $$=$$ Rs. $$0.083$$.

Solve:
$$31\% \,of\,40$$

$$31\%$$ of $$40$$

$$\Rightarrow \dfrac{31}{100}\times 40$$

$$\Rightarrow \dfrac{31}{10}\times 4$$

$$=3.1\times 4$$

$$=12.4$$

$$\therefore 31\%$$ $$40$$ is $$12.4$$

A person has money to buy $$25$$ cycles worth Rs. $$500$$ each. How many cycles he will be able to buy if each cycle is costing Rs. $$125$$ more?

Total cost of buying cycle

$$\\=25\times500=12500$$

now cost of each cycle=625Rs

$$\\\therefore\>no\>of\>cycles\>can\>be\>\\bought\>now=(\frac{12500}{625})\\=20$$

If the cost of $$7\ m$$ of cloth is $$Rs. 1470$$, find the cost of $$5\ m$$ of clothe.

( 5 * 1470 ) / 7 = 1050 Rs

If the $$S.P$$ is greater than the $$C.P$$ there is____________

If $$S.P> C.P $$ then

Profit $$=S.P-C.P>0$$

$$\implies $$Profit will be there

If $$M.P=x$$ and $$S.P=y$$, then $$d$$%=?

$$\textbf{Step-1: Apply the concept of percentage.}$$

$$\text{We have,}$$

$$\text{M.P. = x}$$ $$S.P=y$$ $$\text{if}$$ $$\left( x>y \right) $$ $$\text{then}$$

$$d\%$$ $$=\left( \dfrac { x-y }{ x } \right) \times 100$$ $$\boldsymbol{[\because\textbf{Discount =}\left( \dfrac { M.P-S.P }{ MP } \right)\times 100]}$$

$$\textbf{Hence, the discount is obatined}$$

Kirti bookstore sold books worth Rs.$$2,85,891$$ in the first week of june and books worth Rs.$$4,00,768$$ in the second week of the month.How much was the sale for the two weeks together?In which week was the sale greater and by how much?

Total sale in two weeks$$=$$Sale in first week$$+$$Sale in second week

$$=2,85,891+4,00,768=6,86,659$$

So, total sale in two weeks is Rs.$$6,86,659$$

Now, Sale on week $$1=$$Rs.$$2,85,891$$

Sale on week $$2=$$Rs.$$4,00,768$$

So, sale on week $$2>$$Sale on week $$1$$

Let's find the difference in sales of week$$\,2$$ and week$$\,1$$

$$=4,00,768-2,85,891=1,14,877$$

So, sale on week$$2$$ is greater than the sale on week $$1$$ by Rs.$$1,14,877$$

The SP of a product is $$480$$ and Loss is $$30$$ find CP

The SP of product is $$480$$

The Loss of product is $$30$$

The CP of product is $$SP+LOSS=480+30=510Rs.$$

A shop keeper bought a bicycle for $$Rs.3000$$ and sold the same for $$Rs.3400$$. How much was his profit?

Cost price = ₹3000
Selling price =₹3400

therefore,
Profit = Selling price - Cost price
Profit = ₹(3400-3000)

= ₹400

Express the following precentages as ratios in the reduced form.
$$0.64\%$$

0.64%=$$.\frac{0.64}{100}=\frac{64}{100\times 100}=\frac{4}{625}$$
1188325_1344320_ans_f9b1f7846425476da67119d46fc8075f.jpg

$$40\%$$ of $$250$$

$$\dfrac{40}{100}\times250\\4\times 25=100$$

Find the value of x if
$$8\%$$ of Rs.x is $$Rs.100$$

$$8\%$$ of $$Rs.x$$ is $$Rs.100$$

$$\dfrac{8}{100} \times x = 100 \Rightarrow x = \dfrac{100 \times 100}{8} = 1250$$

What is $$15\%$$ of $$20$$ ?

$$15\%$$ of $$20 = \dfrac{15}{100} \times 20 = 3$$

Simplify:$$15\%$$ of $$920$$

15% of 920= $$\frac{15}{100}\times 920=1.5\times 92$$

$$=138$$

1242658_1508367_ans_e5cc03bdf4774636a5ae10c595ab4be4.PNG

Find the cost price, if :
$$S.P. =Rs.\,340$$ and gain $$= Rs.\,20$$

We know that

C.P. = S.P. – Gain

Substituting the values

$$= 340 – 20$$

$$= ₹\,320$$

Find the value of x if
$$45\%$$ of marks x is $$405.$$

$$45\%$$ of marks x is $$405.$$

$$\dfrac{45}{100} \times x = 405 \Rightarrow x = \dfrac{405 \times 100}{45} = 900$$

Find the value of x if
$$32\%$$ of $$x \,kg$$ is $$400\,kg$$

$$32\%$$ of $$x \,kg$$ is $$400\,kg$$

$$\dfrac{32}{100} \times x = 400 \Rightarrow x = \dfrac{400 \times 100}{32} = 1250$$

Find the cost price, if :
$$S. P. = Rs.\,200$$ and $$loss = Rs.\,50$$

$$S.P. = ₹\,200$$ and $$loss = ₹\,50$$

We know that

C.P. = S.P. + loss

Substituting the values

$$= 200 + 50$$

$$= ₹\,250$$

Sachin and Sanjana are calculating $$23\%$$ of $$800.$$
Now calculate $$52\%$$ of $$700$$ using both the ways described above. Which way do you find easier ?

$$Method\ 1$$:

$$52\%$$ of $$700 = (1\% \,of \,700) \times 52$$

$$= (0.01 \times 700) \times 52$$

$$= 7 \times 52$$

$$= 364$$

$$Method\ 2$$:

$$52\%$$ of $$700 = \dfrac{52}{100} \times 700$$

$$= 0.52 \times 700$$

$$ = 364$$

I find the second way easier.

______ is charged on the sale of an item by the government and to the bill amount.

$$\underline{\text{Sale tax}}$$ is charged on the sale of an item by the government and to the bill amount.

Sale tax $$= 5 \%$$ of ________.

Sale tax $$= 5\%$$ of Bill amount

What is $$100\%$$ of $$500$$ ?

$$\Rightarrow 100\%$$ of $$500$$

$$= \dfrac{100}{100} \times 500 = 500$$

Jyosana bought a product for $$Rs. \ 3,155$$ including $$4.5 \%$$ sales tax. Find the price before tax was added.

as per question,
Suppose, the price of the product before sale tax $$=Rs.\ x$$
Now, $$x+x \times \dfrac{45}{100}=3155$$
$$x+\dfrac{x \times 45}{1000}=3155$$
$$x=\dfrac{3155 \times 1000}{1045}=Rs.\ 3019.1387$$

Music $$CD$$ originally priced at $$Rs\ 120$$ is on sale for $$25\%$$ off. What is the $$S.P.$$ ?
Sonia and Rahil have different ways of calculating the sale price for the items they bought.
As you work on the next problem, try both of these methods to see which you prefer.

As per question,
Original price of $$CD=Rs\ 120$$
$$25\%$$ discount on $$Rs\ 120$$.
If the sale is applicable $$=120\times \dfrac{25}{100}=Rs\ 30$$
Discount $$=Rs\ 30$$
So, selling price after discount.
$$Rs\ 120-Rs\ 30=Rs\ 90$$

What is $$800\%$$ of $$800$$ ?

$$\Rightarrow 800\%$$ of $$800$$

$$= \dfrac{800}{100} \times 800 = 6400$$

Find out $$8\%$$ of $$25\,kg.$$

$$\Rightarrow 8\%$$ of $$25\,kg = \left ( \dfrac{8}{100} \times 25 \right ) kg$$

$$ = 2 \,kg$$

Write as a percentage :
$$1.63$$

Ans :- 163%

In order to write 1.63 in percentage , multiply it with hundred.

So, 1.63 = 1.63 x 100% = 163%

At a toy shop price of all the toys is reduced to $$66\%$$ of the original price.
What is the sale price of a toy that originally costs $$Rs\ 90$$?

As per question
When price reduced to $$66\%$$ of the original price,
Then the price $$=90-\dfrac{66}{100}\times 90=Rs\ 30.6$$

The table shows the cost of sunscreen of two brands with the without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate each brand.
Cost (in Rs.) Cost $$+$$ tax
$$1\ .X\ (100\ gm)$$ $$70$$ $$75$$
$$2.\ Y\ (100\ gm)$$ $$62$$ $$65$$

As per question,
Brand $$X$$ sunscreen cost $$=Rs.\ 70$$
And with sales tax$$=Rs.\ 75$$
Now, sales tax paid $$=Rs.\ 75-Rs.\ 70=Rs.\ 5$$
Again,
Brand $$Y$$ sunscreen cost $$=Rs.\ 62$$
And with sales tax$$=Rs.\ 65$$
Now, sales tax paid $$=Rs.\ 65-Rs.\ 62=Rs.\ 3$$
So, great sales tax rate $$=$$Brand $$X$$
Now, sales tax for brand $$X=\dfrac{5}{70} \times 100=7.14 \%$$
Now, sales tax for brand $$Y=\dfrac{3}{62} \times 100=4.84 \%$$

Mohit sold a T.V. for Rs. $$3,600$$, gaining one-sixth of its selling price. Find the gain (in Rs.)

Given, $$ S.P. = Rs 3600 $$
$$ Gain = \dfrac {3600}{6} = Rs 600 $$

An article marked at $$Rs. 1000$$ is sold at a discount of $$20\%.$$. Find selling price of the article in $$Rs.$$

Since, Market price of an article $$= Rs. 1000$$

Discount% $$=20$$%

Discount $$= 1000\times \frac {20}{100}=Rs. 200$$

Selling price $$=$$ Market price $$ -$$ Discount

$$= 1000 - 200 = Rs. 800$$

A dealer is selling an article at a discount of $$5$$ $$\%$$ on the marked price and its marked price is Rs. $$140$$. What is the cost price, if the marked price is $$12\%$$ above the cost price?

Let the cost price be Rs. $$x$$

$$12\%$$ above $$=$$ Rs. $$1.12x$$

$$\Rightarrow 1.12x=140$$

$$\Rightarrow x=\dfrac {140\times 100}{112}=$$ Rs. $$125$$

Therefore, the cost price of an article is Rs. $$125$$.

An article marked at Rs. 450 is sold at a discount of 20%. Find the selling price of the article.

Discount=$$20\%$$ of $$450$$=$$\dfrac{20}{100}\times 450=90 Rs.$$
S.P=Marked Price-Dicount
S.P.$$=450-90=360 Rs.$$

An article marked at Rs. 450 is sold at a discount of 20%. Find the discount on the article.

Discounted Price =$$20\%$$ on $$450$$
$$\Rightarrow \dfrac {20}{100}\times 450=90 Rs.$$

A shopkeeper allows $$10 \%$$ discount on his article. What price must he mark on an article, which costs him $$Rs. \ 750$$, to make a profit of $$20 \% $$?

C.P= $$750$$, Profit= $$20 \%$$
$$S.P=\dfrac{120}{100}\times 750=900 Rs$$
Let the Mark Price of article= $$ Rs \ x $$.
Then
$$M.P \,-\,10\% \times M.P=S.P $$

$$x-(10 \% \ of \ x)=900$$
$$x-\dfrac{10x}{100}=900$$

$$x-\dfrac{10x}{100}=900$$
$$\dfrac{90x}{100}=900$$
$$x=\dfrac{900\times 100}{90}$$
$$x=1000 Rs.$$

A trader gives $$25 \%$$ discount on his articles and still makes a profit of $$25 \%$$. Find his profit per cent, if he sells his articles at $$10 \%$$ discount.

Lets marked price of goods Rs. $$100$$
After getting $$25\%$$ discount selling price $$=100-25=75$$ Rs
After $$25\%$$ profit cost price$$\dfrac{100}{100+gain}S.P=\dfrac{100}{100+25}75=60$$ Rs
After $$10\%$$ discount market price $$=100-10=90$$ Rs
Profit $$=90-60=30$$ Rs
$$\%$$ of profit $$=$$ $$\dfrac{30\times 100}{60}= 50$$ $$\%$$

A firm, dealing in furniture, allows $$4\%$$ discount on the marked price of each item. What price must be marked on a dining table which costs Rs.$$400$$ to assemble, so as to make a profit of $$20\%$$?

Profit given $$=20\%$$
Thus ,S.P $$=$$ $$\dfrac{120\times400}{100}= 480$$
Discount given $$=4\%$$
Then M.P $$=$$ $$\dfrac{100}{100-discount}\times S.P$$

So M.P $$=$$ $$\dfrac{100}{100-4}\times 480$$ $$=$$ $$\dfrac{100}{96}\times 480$$ $$=500$$ Rs

Hence, M'P $$=$$ Rs.$$500$$

Find which of the following discount series is better for the customer :
$$(i) 30\%, 20\%,$$ and $$10\%; \\$$
$$(ii) 25\%, 20\%,$$ and $$15\%.$$

(1) M.P is Rs. $$ 100$$
so selling price after $$30\%$$ discount $$=$$ $$100-30=$$ Rs. $$70$$
There after selling price $$20\%$$ discount =$$\dfrac{70\times 80}{100}=$$ Rs. $$ 56$$

There after selling price $$10\%$$ discount =$$\dfrac{90\times 56}{100}=$$ Rs. $$50.40$$

(ii)1) M.P is Rs. $$100$$
so selling price after $$ 25\%$$ discount =$$100-25=$$ Rs. $$75 $$
There after selling price $$20$$% discount =$$\dfrac{75\times 80}{100}= $$ Rs. $$60$$

There after selling price $$15\%$$ discount $$=$$ $$\dfrac{85\times 60}{100}=$$ Rs. $$51$$
So, costumer get lower cost on (i) option is better

A shopkeeper allows two successive discounts of $$10\%$$ and $$15\%$$ on his articles. If he gets Rs. $$459$$ for an article, find its marked price.

Successive Discounts given are $$10\%$$ and $$15\%$$

$$S.P. = M.P. \times \dfrac{100-10}{100} \times \dfrac{100-15}{100}$$

$$459 = M.P. \times \dfrac{90\times85}{10000}$$

$$M.P. = \dfrac{459}{0.765}$$

$$\Rightarrow$$ $$M.P. = 600$$

The list price of a watch is Rs.A customer gets two successive discounts, the first being 10%. Calculate, in percentage, the second discount, if the customer pays Rs 306 for it.

List price of watch Rs 400 (given)
After First discount price =$$\dfrac{400\times 90}{100}= 360$$Rs
Then second discount = 360-306=54 Rs
% of discount =$$\dfrac{54\times 100}{360}= 15$$%

Govind & Murari started a business with equal capitals. Govind terminated the partnership after 7 months. At the end of the year they earned a profit of RsFind the difference in each profit

Let they invested x Rs .
Govind invested x Rs. for 7 month
And Murarix Rs. x invested for 12 month
$$\therefore$$ Profit sharing ratio = 7x : 12x = 7 : 12
Total profit at the end of month=7600 Rs.
$$\therefore$$ Govind's profit = $$ \dfrac{7}{7+12}\times 7600=2800$$
Murari's profit = $$\dfrac{12}{7+12}\times 7600=4800$$

The difference in each profit: Rs.$$2000$$.

A wholesaler allows a discount of 20% on the list price to a retailer who sells it at 5% discount on the list price. If a customer paid Rs. 114 for an article, what profit is made by the retailer? Find, also the retailer's percentage profit on his cost.

Lets wholesaler list prices is $$Rs 100$$
Then wholesaler gives $$20\% $$ discount to retailer.
Then selling price to retailer $$= 100-20=Rs 80$$
Retailer sell $$5\%$$ to customer discount on list price $$=Rs 5$$
Then, retailer selling price $$= 100-5 =Rs 95$$
As per question, customer paid $$Rs 114$$ to retailer
Then list price $$=\cfrac{100\times 114}{95}= 120$$
Then C.P of retailer $$=\cfrac{80\times 120}{100}= 96$$
Profit gain by retailer $$=114-96=Rs 18$$
$$\%$$ of profit =$$\dfrac{18\times 100}{96}= 18.75\%$$

A dealer is selling an article at a discount of $$5\%$$ on the marked price. What is the selling price, if the marked price is Rs. $$140$$?

Lets marked price be Rs. $$100$$
Then selling price $$=100-5=95$$
If selling is Rs. $$140$$
when M.P=100 then S.P.=95
when M.P=1 then S.P.=$$\dfrac{95}{100}$$
when M.P=140 then S.P $$=\dfrac{140\times95}{100}=$$ Rs. $$133$$ $$\text{[using unitary method]}$$

A shopkeeper allows $$20\%$$ discount on the advertised prices of his goods and still makes a profit of $$12\%$$ on his cost price. Calculate the advertised price of an article on which gains Rs. $$135$$.

Lets cost price be $$X$$
$$12 \%$$ of $$X$$ (profit ) $$=135$$ ....Given
Therefor $$X=$$ $$\dfrac{135\times 100}{12}=$$ Rs. $$ 1125 $$
$$\text{C.P.}$$ $$=$$ Rs. $$1125$$
$$\text{S.P.}$$ $$ =1125+135=1260 $$
$$\text{S.P.}$$ $$= 1-20\%$$ of $$\text{M.P.}$$
$$1260=$$ $$\dfrac{4}{5}$$ of $$\text{M.P.}$$
$$\text{M.P.}$$ $$=$$ $$\dfrac{1260\times 5}{4}= 1575 $$

David started a business establishment by investing Rs.After 4 months William entered into a partnership by investing a certain amount. At the end of the year, the profit was shared in the ratio 9 :Find how much money was invested by William.

Let William invested Rs.x

Profit sharing ratio $$= 15000 \times 12 : 8x = 1; 80,000 = 8x$$
Also profit ratio $$= 9 : 8 $$

$$\therefore$$ ATP $$180000 : 8x = 9 : 8$$
$$\displaystyle \Rightarrow \frac{180000\times 8}{9\times 8}=x$$

$$\Rightarrow x=Rs.20,000$$

Find discount in percent when M.P.=Rs.500 and S.P.=Rs.425

Marked Price = Rs 500
Selling Price = Rs 425
Discount = $$500 - 425 = 75$$
Discount (%) = $$\dfrac{75}{500} \times 100 = \dfrac{75}{5} = 15$$ %

Find discount in percent when M.P.= Rs.900 and S.P.=Rs.873

Marked Price = Rs 900
Selling Price = Rs 873
Discount = $$900 - 873 = 27$$
Discount (%) = $$\dfrac{27}{900} \times 100 = \dfrac{27}{9} = 3$$ %

Fins a single discount equivalent (in $$\%$$) to the discount series $$25\%, 20\%$$ and $$10\%$$

Let the marked price of the article be Rs. $$100$$.

Then a single discount equivalent to the discount series is
$$\displaystyle =(100-\frac{100-25}{100}\times \frac{100-20}{100}\times \frac{100-10}{100}\times 100)\%$$
$$\displaystyle =(100-\frac{75}{100}\times \frac{80}{100}\times \frac{90}{100}\times 100)\%$$
$$\displaystyle =(100-\frac{3}{4}\times \frac{4}{5}\times \frac{9}{10}\times 100)\%$$
$$=(100 - 54)\%$$
Hence, the given discount series is equivalent to a single discount of $$46\%$$.

The marked price of a woolen coat is RsIt is sold at a discount of $$15 \%$$ The shopkeeper has allowed a further discount of 5% due to off season Find the selling price (in Rs) of the coat

Marked price = Rs. $$2000$$ 1st discount = $$15% of Rs.2000 =$$ Rs.$$\displaystyle \frac{15}{100}\times 2000=Rs.300$$
$$\therefore$$ The reduced marked price after the 1st discount = Rs. $$2000 - Rs.300 = Rs.1700$$
2nd discount due to off-season = $$5$$% of Rs.$$1700$$ = Rs. $$\displaystyle \frac{5}{100}\times 1700=Rs.85$$
Hence the final reduced price after the 2nd discount
= $$Rs.1700 - Rs.85$$
= $$Rs. 1615 = $$$$S.P.$$
Hence the required $$S.P.$$ of the coat is Rs.$$1615$$

A man buys an article and sells it at a profit of $$20$$%. If he would buy it at $$20$$% less and sell it for Rs $$75$$ less he would have gained $$25$$%. What is the cost price (in Rs) of the article?

Let the C.P. of the article be Rs. x

He makes a profit of 20%

Hence,

S.P. = Rs.$$\displaystyle \frac{120x}{100}$$

$$=Rs.\frac{6x}{5}$$

If he would buy it at 20% less then new C.P. = Rsx $$\displaystyle \left (

1-\frac{20}{100} \right )$$

$$=Rs.x\left ( 1-\dfrac{1}{5} \right

)$$

$$=Rs.\dfrac{4x}{5}$$

He would sell it for Rs. 75 less Then the new S.P. = Rs. $$\displaystyle \left ( \frac{6x}{5}-75 \right )$$

He gains 25% then the new S.P. = Rs. $$\displaystyle \frac{125}{100}\times \frac{4x}{5}=Rs.x$$

Hence,

$$\displaystyle \frac{6x}{5}-75=x$$

$$\Rightarrow \dfrac{6x}{5}-x=75$$

$$\Rightarrow \dfrac{x}{5}=75$$

Hence the required C.P. = Rs.375

Tanoj & Manoj started a business by investing Rs 75000 and Rs 90000 respectively. It was decided to pay Tanoj a monthly salary of Rs 1875 as he was the active partner. At the end of the year if the total profit is Rs 39000 find the difference of their profits

Profit sharing ratio = 75000 : 90000 = 5 : 6 Total profit = Rs. 39000
Salary of Tanoj = $$12 \times 1875 = Rs.22500$$
Profit left =$$ Rs.39000 - Rs.22500 = Rs.16500$$
Tanoj's profit = $$\dfrac{5}{11}\times 16500=Rs.7500$$
$$\therefore$$ Total profit of Tanoj =$$ 22500 + 7500 = Rs.30000$$
Manoj's profit = $$\dfrac{6}{11}\times 16500=Rs.9000$$

Difference=21000

Nitesh & Jitesh invested Rs 15000 and Rs 18000 respectively in a business. If the total profit at the end of the year is Rs 8800 and Nitesh being an active partner gets an additional 12.5% of the profit, find the total profit of Nitesh in Rs

Profit sharing ratio = 15000 : 18000 = 5 : 6 Total profit = 8800
Nitesh gets 12.5% of the profit $$=\dfrac{12.5}{100}\times 8800=Rs.1100$$
Net profit = $$8800 - 1100 = Rs. 7700$$
Nitesh share in profit $$ =\dfrac{5}{5+6}\times 7700=Rs.3500$$
Total profit of Nitesh $$= 3500 + 1100 = Rs. 4600$$

David started a business establishment by investing RsAfter 4 months William entered into a partnership by investing a certain amount. At the end of the year the profit was shared in the ratio 9 :Find how much money was invested by william in Rs

Let william invested Rs.x
Profit sharing ratio = $$15000 \times 12 : 8x = 1,80,000 : 8x $$
Also profit ratio = $$9 : 8$$
$$\therefore 180000 : 8x = 9 : 8$$
$$\Rightarrow \dfrac{180000\times 8}{9\times 8}=x\Rightarrow x=Rs.20,000$$

M: The price of T.V. set inclusive of Sales Tax of 9% is Rs. 13,Find its marked price.
A: If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?

Then M+A is

M. Let the M.P is Rs x

Then according to the question

$$\rightarrow x+9\% of x=13407$$

$$\Rightarrow x+\frac{9}{100}=13407$$

$$\Rightarrow \frac{109x}{100}=13407$$

$$\Rightarrow x=\frac{13407\times 100}{109}$$

$$\Rightarrow x=Rs.12300$$

A .If sales tax increased 13% then

Sales price$$=12300+13 \% of 12300$$

Sales price$$=12300+\frac{13}{100}\times 12300$$

Sales price$$=12300+1599=Rs.13899$$

so customer pay$$=13899-13407=Rs.492 $$ More

Then $$M+P=12300+492= Rs.12792$$

The marked price of two articles A and B together is $$\text{Rs. } 6,000$$. The sales tax on article A is $$8\%$$ and that on article B is $$10\%.$$ If on selling both the articles, the total sales tax collected is $$\text{Rs. } 552,$$ find the marked prices of each of the articles A and B.

let the marked price of A $$=\text{Rs. }x$$

then marked price of B$$=\text{Rs. }(6000-x)$$

Sales tax on A is $$8\%$$ of x$$=\dfrac{8}{100}\times x=\dfrac{2x}{25}$$

Sales tax on B is $$10\%$$ of $$6000-x$$ $$=\dfrac{6000-x}{10}$$

According to the question

$$\Rightarrow \dfrac{2x}{25}+\dfrac{6000-x}{10}=552$$

$$\Rightarrow \dfrac{8x+60000-10x}{100}=552$$

$$\Rightarrow 60000-2x=55200$$

$$\Rightarrow 2x=4800$$

$$\Rightarrow x=2400$$

$$\therefore$$ Marked Price of A $$=\text{Rs. }2400$$

Marked Price of B $$=6000-2400=\text{Rs. }3600$$

Increases to 15%

Given - Selling Price (S.P): Rs. 8,250 ; Sales Tax: 10%

Solution:

Let the marked price (M.P) of the article be $$Rs. x$$

$$ \mbox{Selling Price} = \mbox {Marked Price + Tax}$$

$$ 8250 = x + \dfrac{10}{100} x $$ = $$ 1.1 x$$

$$ \therefore x = 7500 \Rightarrow M.P = Rs. 7,500 $$

If Sales Tax is increased from 10% to 15%, then the S.P of the article will also increase.

Hence the customer will have to pay more i.e the difference in amount of tax.

Increase in tax = $$15$$% - $$10$$% = $$5$$%

Increase in $$S.P = M.P \times 5$$% = $$ 7500 \times \dfrac{5}{100}$$ = $$Rs. 375$$

A person bought an article and sold it at a loss of 15%. If he bought it for 20% less and sold it for Rs. 114 more he would have had profit of 30% . Find the cost price of the article.

Let's say CP was x
SP$$ = x - 15\% $$ of $$x =x-\frac{15}{100}x=\frac{85x}{100}= 0.85x$$
If he bought it for 20% less,
CP $$= x - 20\%$$ of $$x = x-\frac{20x}{100}=\frac{80x}{100}=0.8x$$
New $$ SP = 0.85x + 114$$
Now gain $$ = 30\% $$ of $$0.8x$$

then $$S.P-C.P=gain $$
$$\Rightarrow 0.85 x + 114 - 0.8x = \frac{30}{100}\times 0.8 x$$
$$\Rightarrow 0.05x + 114 = 0.24x$$
$$\Rightarrow 0.19x = 114$$
$$\Rightarrow x =\frac{114}{0.19}= 600$$
then CP =Rs. 600

A hawker sells orange at a profit of $$25\%$$. If he reduces the selling price of each orange by $$60$$ paise, he earns a profit of $$5\%$$. Find the final selling price of each orange.

Let CP = $$x$$ paise
Initial SP $$= x + 25\% \ of\ x = 1.25 x$$

New SP$$ =( 1.25 x - 60)$$ paise
New gain $$= 5\% \ of \ x$$

$$\Rightarrow New\ SP - CP = 0.05x$$
$$\Rightarrow 1.25 x - 60 - x = 0.05x$$

$$\Rightarrow 0.25 x - 60 = 0.05x$$

$$\Rightarrow 0.25 x - 0.05x = 60$$
$$\Rightarrow 0.2 x = 60$$
$$\Rightarrow x = \dfrac{60}{0.2} = 300 $$

So, the CP $$=300\ paise$$

Hence, final selling price

$$=1.25x-60$$

$$=( 1.25 \times 300 - 60)\ paise = 315 \ paise = Rs. 3.15$$

If the marked price of an article is $$50\%$$ above the cost price, when marked price is increased by $$20\%$$ and selling price is increased by $$20\%$$ then the profit is doubled. If the original marked price is $$Rs.300$$ then what is the original selling price?

Given,
$$MP = Rs.300$$
Marked price was $$50\%$$ above the cost price.

Let $$CP$$ be $$y$$

So, $$MP= y + 50\%\ of\ y $$

$$\Rightarrow y+\dfrac{50}{100}\times y= 300$$

$$\Rightarrow y = Rs. 200$$

Let the $$SP$$ was $$X$$.

$$\therefore \ Profit=Rs.(X-200)$$

New $$MP=Rs.( 300 + 20\%\ of\ 300) =Rs.(300+\dfrac{20}{100}\times 300)= Rs.360.$$

So,New $$SP=X+20\%\ of\ X=X+\dfrac{20}{100}X=1.2X$$

$$\therefore Profit=Rs.(1.2X-200)$$

Now, according to question,
$$\Rightarrow 1.2 X - 200 = 2\times (X-200)$$
$$\Rightarrow 1.2X - 200 = 2X - 400$$
$$\Rightarrow 0.8X = 200$$
$$\Rightarrow X = 250$$
Thus, original selling price was $$Rs.250$$

The price of a TV is $$Rs. 13,000$$. The sales tax charged on it is at the rate of $$12$$%. Find the amount that Vinod will have to pay if he buys it.

$$\textbf{Hint: Using the percentage and price relation.}4$$

$$\textbf{Step 1: Find the tax amount.}$$

$$\text{Given}$$

$$\text{Price of TV}=13,000$$

$$\text{Sales tax percentage}12\%$$

$$\text{Note: Sales tax is charged on the cost price of an item and is added to the bill}$$

$$\text{Tax amount=sales tax percentage}$$ $$\times$$ $$\text{Price}$$

$$=12 \% \times 13,000$$

$$=\dfrac{12}{100} \times 13000$$

$$=12 \times 130$$

$$\text{Tax amount}$$ $$=1560$$

$$\textbf{Step 2: Find the bill amount.}$$

$$\text{Bill amount=price of TV+ Tax amount}$$

$$=13000+1560$$

$$=14560$$

$$\textbf{Vinod will have to pay the amount is 14560.}$$

A tape recorder is sold at $$Rs. 5,225$$ after being given a discount of $$5$$%. What is its marked price?

We are given that the discount is $$5$$%. This means that for $$Rs. 100$$, the discount is $$Rs. 5$$.
Therefore, selling price $$= Rs. 100 - Rs. 5 = Rs. 95$$.
Thus on a selling price of $$Rs. 95$$, the marked price is $$Rs. 100$$.
On a selling price of $$Rs. 5,225$$, the marked price $$= \dfrac {100}{95}\times 5225 = 5500$$.
Therefore, marked price of the tape recorder is $$Rs. 5,500$$.

An article marked $$Rs. 800$$ is sold for $$Rs. 704$$. Find the discount and discount percent.

M.P of article = $$800$$ Rs
S.P of article = $$704$$ Rs
Discount $$=$$ M.P. - S.P.
$$=800 - 704=96$$ Rs

Discount % = $$\dfrac{\text{Discount amount}}{M.P} \times 100$$.
Discount % = $$\dfrac{96}{800} \times 100 = 12$$%.

The marked price of an gift item is $$Rs. 176$$ and sold it for $$Rs. 165$$. Find the discount percent.

Marked Price$$ = 176, $$ Selling Price $$= 165$$

$$Discount = \cfrac {M.P-S.P}{M.P} $$

$$ \cfrac {176-165}{176} = 0.0625$$ or $$6.25$$%

$$ \therefore $$ discount percent is $$6.25$$%

Find the selling price of a towel of Rs. $$50$$ when a sales tax of $$5\%$$ is added to it.

Given

Marked Price $$= Rs.50$$

Tax $$= 5$$%

Selling price $$=$$ Marked Price $$+$$ Tax

$$ = Rs.\left(50 + \cfrac {5}{100} \times 50\right) $$

$$=Rs. 52.5$$

$$\therefore $$ selling price of towel is $$Rs.52.5$$

A shopkeeper bought an article for Rs. $$3,450$$. He marks the price of the article $$16\%$$ above the cost price. The rate of sales tax charged on the article is $$10\%$$. Find the :
(i) marked price of the article
(ii) price paid by a customer who buys the article.

Cost price of the article $$=$$ Rs. $$3,450$$.
(i) Marked price $$=$$ Cost Price $$+$$ % marked above cost price

$$=$$ Rs. $$3,450 + \dfrac{16}{100} \times 3,450$$
$$=$$ Rs. $$4,002$$

(ii) Price paid by the customer $$=$$ Marked Price $$+$$ Tax charged

$$=$$ Rs. $$4,002 + \dfrac{10}{100} \times 4,002$$
$$=$$ Rs. $$4,402.20$$

If printed price is $$Rs. 50$$ and selling price is $$Rs. 45$$, then find the amount of discount

Given, Printed price $$= Rs. 50$$
$$S.P. = Rs. 45$$
$$\therefore Discount = 50 - 45 = Rs. 5$$

Calculate the education cess at the rate of $$3$$% on the income tax $$Rs. 900$$ for the F.Y. $$2012 - 13$$

Given,

Income tax $$= \text{Rs. }900$$
Rate $$ = 3 \%$$

$$\therefore$$ Education cess $$= 900 \times \dfrac {3}{100}$$
$$= \text{Rs. }27$$

Mr. Albert's gross annual income is Rs. $$5,00,000$$ for F.Y. $$2012-13$$. His annual savings in this year are as follows :
(a) L.I.C. premium Rs. $$70,000$$.
(b) Contribution towards P.F. Rs. $$12,000$$
(c) P.P.F. Rs. $$30,000$$
(d) N.S.C. Rs. $$10,000$$
Find his taxable income and income tax for F.Y. $$2012-13$$.

Total annual income of Mr. Albert $$=$$ Rs. $$5,00,000$$.
Annual savings :
(a) L.I.C. premium $$=$$ Rs. $$70,000$$
(b) Contribution towards P.F. $$=$$ Rs. $$12,000$$
(c) P.P.F. $$=$$ Rs. $$30,000$$
(d) N.S.C. $$=$$ Rs. $$10,000$$
Total savings $$=$$ Rs. $$1,22,000$$
Total taxable income $$=$$ Rs. $$\left( 5,00,000-1,22,000 \right)$$ $$ =$$ Rs. $$3,78,000$$
Now, Income tax for F.Y. $$2012-13$$.
For income upto Rs.$$2,00,000$$ at $$0\%=$$ Rs. $$ 00.00$$
For income Rs. $$\left( 3,78,000-2,00,000 \right) $$
$$=$$ Rs. $$1,78,000$$ at $$10\%$$
$$=\dfrac { 178000\times 10 }{ 100 } =$$ Rs. $$17,800$$
Total income tax $$=$$ Rs. $$17,800$$
Mr. Albert will have to pay income tax Rs. $$17,800$$.

A person has a gross annual income of Rs. $$3,00,000$$ for F. Y. $$2012-13$$. Under Section $$80 C$$, Rs. $$1,00,000$$ is deducted from the gross annual income. Find his taxable income for F. Y. $$2012-13$$.

Gross annual income of a person $$=$$ Rs. $$3,00,000$$.
Deduction from the gross annual income $$=$$ Rs. $$1,00,000$$
Taxable income $$=$$ Rs. $$\left(3,00,000 - 1,00,000\right)$$ $$=$$ Rs. $$2,00,000$$.

Mr. Kale $$(52$$ years old$$)$$ has taxable income of Rs. $$5,05,000$$ in financial year $$2012-13$$. Calculate the net income tax payable.

According to taxation rule, income upto Rs. $$1,80,000$$ is non taxable income from Rs. $$1,80,001$$ to Rs. $$5,00,000$$ is charged at $$10\%$$ p.a. $$= \dfrac{3,20,000}{100} \times 10$$
$$=$$ Rs. $$32,000$$
Income above Rs. $$5,00,001$$ to Rs. $$8,00,000$$ is charged at $$20\%$$ p.a.
$$= \dfrac{5,000 \times 20}{100}$$
$$=$$ Rs. $$1,000$$
Total income tax payable $$=$$ Rs. $$(32,000 + 1,000)$$
$$=$$ Rs. $$33,000$$

The marked price of an article is Rs. $$900$$. It is sold at a discount of $$10\%$$. Find the discount allowed on the article.

Marked price of an article $$=$$ Rs. $$900$$
Rate of discount $$=10\%$$
Discount $$=\dfrac { \text{Rate of discount}\times M.P. }{ 100 }$$
Discount $$ =Rs.\dfrac { 10\times 900 }{ 100 } =Rs.90$$
Discount allowed on the article is $$Rs.90$$.

Naseem runs a readymade garment shop. He marks the garment at such a price even after allowing a profit of $$12.5$$%,he makes a discount of $$10$$%. Find the marked price of a suit which costs him $$1470$$

$$CP=1470Rs$$

$$Profit=10\%$$

$$SP=1470\times \dfrac{110}{100}$$

$$SP=1617Rs$$

$$Discount=12.5\%$$

$$MP=1617\times \dfrac{100}{87.5}$$

$$MP=1848Rs$$

The marked price of the suit$$=1848Rs$$

Suresh purchased the following articles from Swarah Khadi Bhandar. The rebate on each article is $$20$$%. Find the total amount he paid at the time of purchase.
$$2$$ towels for $$Rs. 90$$ each
$$3$$ shirts for $$Rs. 220$$ each
$$4$$ trousers for $$Rs. 290$$ each

Articles	Name	Cost per item (Rs)	Total
$$2$$	Towel	$$90$$	$$180$$
$$3$$	Shirt	$$220$$	$$660$$
$$4$$	Trouser	$$290$$	$$1160$$
			$$Rs. 2000$$

$$\therefore Rebate = 2000\times \dfrac {20}{100} = Rs. 400$$
$$\therefore$$ Total amount to be paid $$= 2000 - 400 = Rs. 1600$$.

Observe the table and state whether the income tax is to be paid or not with reason for the following persons having taxable income of F.Y. $$2012-13$$ as given below:
Person Age (in year) Taxable income The tax is to be paid or not Reason
Sau. Shalini $$25$$ Rs. $$1,30,000$$
Shri. Dhiraj $$32$$ Rs. $$2,85,000$$
Shri Shashibhai $$80$$ Rs. $$2,70,000$$
Smt. Minakshi $$61$$ Rs. $$2,40,000$$

According to the taxation rule for F.Y. $$2012 - 13$$.

Person	Age (in year)	Taxable income	The tax is to be paid or not	Reason
Sau. Shalini	$$25$$	Rs. $$1,30,000$$	Tax is not to be paid	Taxable income is below basic exemption i.e. Rs. $$2,00,000$$.
Shri. Dhiraj	$$32$$	Rs. $$2,85,000$$	Tax is to be paid	Taxable income is above basic exemption i.e. Rs. $$2,00,000$$.
Shri Shashibhai	$$80$$	Rs. $$2,70,000$$	Tax is to be paid	Taxable income is above basic exemption i.e. Rs. $$2,50,000$$.
Smt. Minakshi	$$61$$	Rs. $$2,40,000$$	Tax is not to be paid	Taxable income is below basic exemption i.e. Rs. $$2,50,000$$.

The marked price of a machine is Rs.$$2,400$$. It is sold at a discount of $$8$$ $$\%$$. Find the discount allowed on the machine.

Marked price of a Machine $$=$$ Rs. $$2,400$$
Rate of discount $$=8$$ $$\%$$
Discount $$=\dfrac { \text{Rate of discount}\times M.P. }{ 100 }$$
Discount $$ =\dfrac { 8\times 2400 }{ 100 } =$$ Rs. $$192$$
Discount allowed on the Machine is Rs. $$192$$.

Taxable income of Smt. Rekha (age $$45$$ years) is Rs. $$6,50,000$$ for the financial year $$2012 - 13$$. Compute the income tax she will have to pay for $$2012 - 13$$

As per income tax slab for the financial year $$2012 - 13$$.
According to taxation rule, income upto, Rs. $$2,00,000$$ is non-taxable income.
From Rs. $$2,00,000$$ to Rs. $$5,00,000$$ is
charged at $$10$$ $$\%$$ $$p.a. = \dfrac {3,00,000\times 10}{100}$$
$$=$$ Rs. $$30,000$$
Income above Rs. $$5,00,000$$ to Rs. $$10,00,000$$ is charged at $$20$$ $$\%$$ p.a.
$$= \dfrac {20}{100} \times (6,50,000 - 5,00,000)$$

$$=30,000$$

Therefore, income tax paid by Smt. Rekha for $$2012-13$$ is Rs. $$30,000+30,000=$$ Rs. $$60,000$$.

The marked price of a DVD is Rs. $$1,200$$. It is sold at a discount of $$4$$$$\%$$. Find the discount allowed on the article.

Marked price of a D.V.D. $$=$$ Rs. $$1,200$$
Rate of discount $$=4$$ $$\%$$
Discount $$=\dfrac { \text{Rate of discount} \times \text{M.P.} }{ 100 }$$
Discount $$ =\dfrac { 4\times 1200 }{ 100 } =48$$
Discount allowed on the D.V.D. is Rs. $$48$$.

Find the total amount if $$12$$% of it is $$1080$$.

Let the total amount be $$x$$.
Given : $$12$$% of the total amount $$=$$ $$1080$$
   $$\dfrac{12}{100} \times x = 1080$$
   $$x = \dfrac{1080 \times 100}{12} =$$ $$9000$$
   $$\therefore$$ The total amount $$=$$ $$9000$$.

A bicycle marked at $$1,500$$ is sold for $$1,350$$. What is the percentage of discount?

Marked Price $$=$$ $$1500$$, Selling Price $$=$$ $$1350$$
Amount of discount $$=$$ Marked Price $$-$$ Selling Price
$$= 1500 - 1350$$
$$=$$ $$150$$
Discount for $$1500 =$$ $$150$$
Discount for $$100 = \dfrac{150}{1500} \times 100$$
Percentage of discount $$= 10$$%

The list price of a frock is $$220$$. A discount of $$20$$% on sales is announced. What is the amount of discount on it and its selling price?

List (Marked) Price of the frock $$=$$ $$220$$, Rate of discount $$= 20$$%
Amount of discount $$= \dfrac{20}{100} \times 220$$
$$=$$ $$44$$
$$\therefore$$ Selling Price of the frock $$=$$ Marked Price $$-$$ Discount
$$= 220 - 44$$
$$=$$ $$176$$.

Moika paid Rs. $$8.25$$ for chips and Rs. $$5.75$$ for chocolates she got Rs. $$7$$ back from the shopkeeper. How much money did she pay?

Money paid for chips $$= Rs. 8.25$$

Money paid for chocolates $$= Rs. 5.75$$

Money returned by the shopkeeper $$= Rs. 7$$

Therefore, money paid by monika $$= Rs. (8.25+5.75)-7$$

$$= Rs. (14 - 7)$$

$$= Rs. 7$$

Vinodh purchased musical instrument for $$12,000$$. If the rate of sales tax is $$8$$%, find the sales tax and the total amount paid by him.

Value of the musical instrument $$=$$ $$12,000$$
Rate of Sales Tax $$= 8$$%
Amount of Sales Tax $$= \dfrac{8}{100} \times 12000$$
$$=$$ $$960$$
Total amount paid by Vinodh including Sales tax $$= 12,000 + 960$$
$$=$$ $$12,960$$

A refrigerator is purchased for $$14,355$$, including sales tax. If the actual cost price of the refrigerator is $$13,050$$, find the rate of sales tax.

Given:

For the refrigerator, bill amount $$=$$ $$14,355$$, Cost price $$=$$ $$13,050$$.
Sales tax $$=$$ Bill amount $$-$$ Cost of the item
$$= 14,355 - 13,050 =$$ $$Rs.1,305$$
Rate of Sales Tax $$= \dfrac{\text{Amount of Sales Tax}}{\text{Cost of the item}} \times 100$$
$$= \dfrac{1305}{13050} \times 100 = 10\%$$

Calculate and fill the table on the basis of the details given below:
No. Product MRP (Rs) % rebate Amount of the rebate (Rs) Amount to be paid (Rs)
(1) Towel
(2) Curtain
(3) 1 kg Biscuits

$$1) Rs18.75, Rs. 106.25$$

$$ 2) Rs 75, Rs 675$$
$$3) Rs 2, Rs 38$$

A dealer allows a discount of Rs 10% and still gains by 10%. What should be the marked price if the cost price is Rs 900?

Let the marked price be $$x$$

Given, $$C.P=Rs \,900$$

And discount $$=$$ $$10\%$$ of $$x$$

$$ = \dfrac{{10}}{{100}}\times x$$

$$=\dfrac{x}{{10}}$$

SP $$=$$ MP $$-$$ Discount

$$=x - \dfrac{x}{{10}}$$

$$ = \dfrac{{9x}}{{10}}$$

Now, Gain $$=$$ S.P $$-$$ C.P

$$\Rightarrow 10\%$$ of CP $$=$$ S.P $$-$$ C.P

$$\Rightarrow$$$$\dfrac{{10}}{{100}}\times 900=\dfrac{9x}{{10}} - 900$$

$$\Rightarrow$$ $$90+ 900 = \dfrac{9x}{{10}}$$

$$\Rightarrow$$ $$x= 1100$$

$$\therefore$$ Marked Price is Rs $$1,100$$

Find the amount of sales tax a customer has to pay.

Given

MP $$= 42,000$$

First Discount $$= 10\%$$

Second Discount $$= 5\%$$

Sales Tax $$= 8\%$$

So,

First Discount $$=$$ $$\dfrac { 10 }{ 100 } \times { 42,000 }$$

$$=$$ $$4,200$$

$$\therefore$$ Standing Amount after first disount $$=\quad 42,000-4,200$$

$$=37,800$$

Second Discount $$= \dfrac { 5 }{ 100 } \times { 37,800 }$$

$$=1,890$$

$$\therefore$$ Standing after second discount $$=37,800-1,890$$

$$ =35,910$$

Now, Payable tax $$=\quad \dfrac { 8 }{ 100 } \times { 35,910 }$$

$$=2,872.80$$

Hence, Customer has to pay Rs $$2,872.80$$ for the sales tax.

Find the amount received when $$300$$ shares of FV $$Rs. 100$$, were sold at a discount of $$Rs. 30$$.

$$FV=Rs.100$$

For discount$$=Rs.30$$

$$MV=Rs.(100-30)=RS.70$$

No. of shares $$=300$$

Amount received$$=Rs.70\times 300=Rs.21,000$$

The list price of a frock is $$Rs. 220$$. A discount of $$20\%$$ is announced on sales. What is the selling price?

Listed price $$=220$$

Discount $$= 20\%$$

$$S.P= Listed\ price(1-\dfrac { discount }{ 100 })$$

$$S.P= 220(1-\dfrac { 20 }{ 100 })$$

$$S.P = Rs.176$$

Selling price $$Rs.176$$

If the price of a book is reduced by $$Rs\ 5$$, a person can buy $$5$$ more books for $$Rs\ 300$$. Find the original list price of the book.

$$\textbf{Step -1: Find the original price of the book.}$$

$$\text{Let the original list price of the book be Rs. }x.$$

$$\text{In Rs. }300,\text{ number of books a person can buy}=\dfrac{300}{x}.$$

$$\text{New cost price of the book}=\text{Rs. }x-5$$

$$\text{Then, number of books can be bought in Rs. }300=\dfrac{300}{x-5}$$

$$\text{According to the question,}$$

$$\dfrac{300}{x-5}=\dfrac{300}{x}+5$$

$$\Rightarrow \dfrac{300}{x-5}=\dfrac{300+5x}{x}$$

$$\Rightarrow 300x=300x+5x^2-1500-25x$$

$$\Rightarrow 5x^2-25x-1500=0$$

$$\Rightarrow x^2-5x-300=0$$

$$\Rightarrow x^2-20x+15x-300=0$$

$$\Rightarrow x(x-20)+15(x-20)=0$$

$$\Rightarrow (x-20)(x+15)=0$$

$$\Rightarrow (x-20)=0\text{ or }(x+15)=0$$

$$\Rightarrow x=20\text{ or }x=-15$$

$$\because\text{Price cannot be negative.}$$

$$\therefore x=20$$

$$\textbf{ Thus, the original list price of the book is Rs. 20.}$$

A vendor bought $$20$$ oranges for $$Rs.125$$ and sold them at $$Rs. 90$$ per dozen. Find his gain or loss percent to the nearest integer.

CP of $$20$$ oranges $$= Rs. 125$$

$$\therefore$$ CP of $$1$$ orange $$= Rs.\cfrac{125}{20}=Rs. 6.25$$

SP of $$12$$ oranges $$=Rs. 90$$

$$\therefore$$ Sp of $$1$$ orange $$= Rs.\cfrac{90}{12}=Rs. 7.5$$

Profit $$=$$ SP-CP $$=Rs. 7.5-Rs. 6.25=Rs. 1.25$$

$$\therefore Profit \% =\cfrac{1.25}{6.25}\times 100=20\%$$

Find the rate of discount when M.P = $$300$$ and S.P = $$240$$.

Given,

$$MP=300$$

$$SP=240$$

$$Discount=MP-SP=300-240=60$$

Discount Rate $$=\dfrac{Discount}{MP}\times 100\%=\dfrac{60}{300}\times 100\%=\dfrac{100}{5}\%=20\%$$

Rate of Discount $$=20\%$$

When the price of a doll is $$\text{Rs.}\ 4$$ per doll, a doll maker supplies $$8$$ dolls per day. If the price rises to $$\text{Rs.}\ 5$$ per doll, he is willing to supply $$10$$ dolls per day. Calculate the price elasticity of supply of dolls.

Price elasticity of supply $$(E_{S}) = \dfrac {P}{Q}\times \dfrac {\triangle Q}{\triangle P}$$,

where $$P$$ is the price,

$$\Delta P$$ is the change in price,

$$Q$$ is the number of items,

$$\Delta Q$$ is the change in the number of products
$$P_i = \text{Rs.}\ 4$$

$$ P_{f} = \text{Rs.}\ 5$$

$$ \Delta P = P_{f} - P_i = \text{Rs.}\ ( 5 - 4) = \text{Rs.}\ 1$$

$$Q_i = 8\ \text{dolls}$$

$$ Q_{f} = 10\ \text{dolls}$$

$$ \Delta Q = Q_{f} - Q_i = (10 - 8)\ \text{dolls} = 2\ \text{dolls}$$
Price elasticity of supply $$(E_{S}) =\dfrac {4}{8}\times \dfrac {2}{1} = 1 $$
The price elasticity of supply is equal to unity.

During Diwali sale, the cost of a table is $$Rs. 870$$ on which $$\dfrac{1}{5}^{th}$$ of the cost is off. The same table lamp is available at an electric shop for $$Rs. 975$$ with a discount $$\dfrac{1}{15}^{th}$$ of the cost. Which is a better deal and by how much?

$$C_{1}=870$$ , $$Discount_{1}=\dfrac{1}{5}^{th} of 870$$

$$C_{2}=975$$ , $$Discount_{2}=\dfrac{1}{15}^{th} of 975$$

Selling Price $$=CP-Discount\times CP$$

$$SP_{1}=870-\dfrac{1}{5}\times 870=696$$

$$SP_{2}=975-\dfrac{1}{15}\times 975=910$$

Therefore the Better deal is Diwali Sale, by $$(910-696)=Rs214$$

A man derives his income from the investment of $$Rs. 4150$$ at a certain rate of simple interest and $$Rs. 3500$$ at $$1%$$ higher. His whole income for $$4$$ years is $$ Rs. 1211$$. Find the rate of interest.

1371017_1036969_ans_4432591de6d24a2abdcdf738f7e70fa7.JPG

Karim sold a shirt at a loss of $$10\%$$. Had he sold it for Rs. $$60$$ more he would have gained $$5\%$$ on it. Find the cost price of the shirt.

Loss $$=10\%$$ , if Selling Price was $$60$$ more Profit $$=5\%$$

Case 1 : $$SP_1=CP-\dfrac{10}{100}\times CP$$

$$=\dfrac{90}{100}\times CP$$

Case 2 : $$SP_2=SP_2+60$$

$$SP_2=CP+\dfrac{5}{100}\times CP$$

$$=\dfrac{105}{100}CP=SP_1+60CP$$

but $$SP_1=\dfrac{90}{100}$$

$$\implies \dfrac{15}{100} CP=60$$

$$\implies CP=400$$

$$\therefore$$ the Cost Price is Rs $$400$$

Find the gain or loss.
C.P. $$=$$Rs. $$435.00$$; S.P. $$=$$ Rs. $$565.00$$.

now, S.P. - C.P = (565.00 - 435.00)Rs.

$$ S.P. - C.P = 130.00 > 0 $$

$$ S.P - C.P > 0 $$

$$ \therefore S.P. > C.P. $$

So, From CP & SP, We gain.

1180637_1069013_ans_68762de55b0f4033939c551f0259a27a.jpg

Arun bought a pair of skates at a sale where the discount given was $$20\%$$. If the amount he pays is $$Rs\ 1,600$$, find the marked price in Rs

Let the marked price be M

discount$$=20\%$$

Price$$=1600Rs$$

M$$=\dfrac{price}{100-discount}\times100=\dfrac{1600}{100-20}\times100=\dfrac{1600}{80}\times100=2000Rs$$

Maizah bought a pair of pants and a briefcase at a departmental store. The sum of the prices of the pants and the briefcase before sales tax was $$ $130.00$$. There was no sales tax on the pants and a $$9%$$ sales tax on the briefcase. The total Maizah paid, including the sales tax, was $$ $136.75$$. What was the price in dollars, of the pants?

$$\Rightarrow$$ Prices of the pants and briefcase before sales tax $$=\$\,130.00$$

$$\Rightarrow$$ Prices of the pants and briefcase after sales tax $$=\$\,136.75$$

$$\therefore$$ Sales tax on pants and the briefcase $$=\$\,136.75-\$\,130.00=\$\,6.75$$

$$\Rightarrow$$ Let $$x$$ be the price of briefcase.

$$\therefore$$ $$9\%\,of\,x=6.75$$

$$\therefore$$ $$\dfrac{9}{100}\times x=6.75$$

$$\therefore$$ $$x=\dfrac{6.75\times 100}{90}$$

$$\therefore$$ $$x=\$\,75$$

$$\therefore$$ Price of briefcase is $$\$\,75$$

$$\Rightarrow$$ Price of pants $$=\$\,130-\$\,75=\$\,55$$

After offering discount of $$10$$% on marked price, a customer gets total discount of $$17$$ rupees. What is the difference between the marked price and the cost price of the item, if the seller still earns a profit of $$53\%$$?

Given discount is $$10\%$$

marked price will be $$17\times \dfrac{100}{10}=170$$

selling price will be $$170-17=153$$

cost price $$=153-153\times \dfrac{53}{100}=81.09$$

difference between the marked price and cost price is $$170-81.09=88.91$$

The price of tractor is lowered by $$20\%$$ to $$Rs. 40000$$. What was the original price? Also find the reduction in price?

Let the original price be $$x$$.

$$80\%\times x=Rs.40000$$

$$ \implies x=Rs.50000$$

Reduction in price$$=Rs.(50000-40000)=Rs.10000$$.

The list price of a frock is $$\text{Rs. }\ 220$$. A discount of $$20\%$$ is announced on sales. What is the amount of discount on it.

Total amount $$=\text{Rs. }220$$

$$20\%$$ of $$220=\dfrac{20}{100}\times 220$$

$$=2\times 22$$

$$=\text{Rs. }44$$

Hence, this is the required value.

A shopkeeper allows $$20\%$$ discount on the marked price of his articles. Find the marked price of an article for which he charged Rs. $$560$$.

Consider M.P of articles $$= ₹\,100$$

Discount on the M.P $$= 20\%$$

S.P of articles $$= 100 – 20 = ₹\,80$$

If S.P of articles is $$₹\,80$$ then $$M.P = ₹\,100$$

If S.P of articles is $$₹\,560$$ then $$M.P = (100 \times 560)/ 80 = ₹\,700$$

The marked prices of an articles is $$Rs.500$$. The shopkeeper gives a discount of $$5\%$$ and still $$m$$ makes a profit of $$25\%$$. Find the cost prices of the article.

We have,

The marked price of an article $$=500\,rs$$

Discount $$=5%$$

Profit $$=25%$$

Let the cost price of an article $$=x\,rs$$

Then,

We know that,

$$Discount\,price=Marked\,price\,-\,\dfrac{discount%}{100}\times Marked\,price$$

$$ =500-\dfrac{5}{100}\times 500 $$

$$ =500-25 $$

$$ =475 $$

Now,

$$Discount=\operatorname{cost}\,price+\dfrac{profit}{\operatorname{cost}\,price\,\times 100}$$

$$ 475=x+\dfrac{25}{100x} $$

$$ 475=x+\dfrac{1}{4x} $$

$$ \dfrac{5}{4}x=475 $$

$$ x=475\times \dfrac{4}{5} $$

$$ x=380\,rs $$

Hence, this is the answer.

A shop gives $$20\%$$ discount. What would the price of each of these be?
A dress market at $$Rs.120$$
A pair of shoes market at $$Rs.750$$
A bag market at $$Rs.250$$

A - Price $$=(\dfrac{100\%-20\%}{100\%})*120=\dfrac{80}{100}*120=96$$

B - Price $$=(\dfrac{100\%-20\%}{100\%})*750=\dfrac{80}{100}*750=600$$

C - Price $$=(\dfrac{100\%-20\%}{100\%})*250=\dfrac{80}{100}*250=200$$

If S.P. of an article is $$\frac{3}{2}$$ of its C.P.,then profit (in percent) is.

Let the cost price be $$x$$.

Since, the selling price $$=\dfrac{3}{2}x$$

We know that

Profit $$ =\dfrac{S.P-C.P}{C.P}\times 100$$

$$=\dfrac{\dfrac{3x}{2}-x}{x}\times 100 $$

$$=\dfrac{\dfrac{x}{2}}{x}\times 100 $$

$$=\dfrac{1}{2}\times 100 $$

$$=50 \% $$

Hence, this is the answer.

Mrs. Goyal has to pay $$4\%$$ sales tax in addition to the price if a certain article. Find the price of her article, if she pays $$Rs.260$$ in all?

Let the price of the article be $$Rs. x$$. Then,

$$x+4\% \ of \ x=260$$

$$x+\dfrac{4}{100}x=260$$

$$x+\dfrac{x}{25}=260$$

$$26x=260 \times 25$$

$$x=10 \times 25$$

$$x=250$$

Thus, the price of the article is $$Rs. 250$$.

The cost price of an article is Rs. $$1600$$, which is $$20\%$$ below the marked price. If the article is sold at a discount of $$16\%$$, then find the marked price.

Given :

Cost price $$=Rs.1600$$

Let Marked price be $$x$$

Then $$\dfrac{80\times x}{100}=1600$$

$$x=2000$$

$$\therefore$$ Marked price $$=Rs\ 2000$$

After allowing a discount of $$7\dfrac{1}{2}\%$$ on the marked price, a toy was sold for Rs. $$555$$. Find its marked price.

Discount$$=7.4\%$$

Selling Price $$=\text{Rs. }555$$

$$\therefore (100-7.4)\%\times$$ Marked price $$=$$ selling price

$$\implies (100-7.4)\%\times$$ Marked price $$ =Rs.555$$

$$\implies 92.6\%\times M.P=555$$

$$\implies$$ Marked price $$=\dfrac{555\times 1000}{926}$$

$$\implies$$ Marked price $$=\text{Rs }599.352$$

Hence, marked price $$=\text{Rs. }600$$ (approx)

A table marked at $$Rs. 15,000$$ is available for $$Rs. 14,400$$. Find the discount given and the discount per cent.

Discount $$=\%\cfrac{15,000-14,400}{15,000}\times 100=4\%$$.

A dealer gave $$9\%$$ discount on an electric fan and charges Rs. $$728$$ from the customer. Find the marked price of the fan.

Consider $$Rs. x$$ as the $$M.P.$$ of the fan
Discount = $$9\%$$

$$\therefore$$ SP = $$Rs. x - Rs. 9\%\ of\ x$$
$$\Rightarrow 728 = \dfrac{91x}{100}$$
$$\Rightarrow x = \dfrac{728\times100}{91}$$
$$\Rightarrow x = 8 \times 100$$
$$\Rightarrow x = 800$$

Therefore, the marked price of the fan is $$Rs.800$$.

A shopkeeper purchased a calculator for Rs. $$650$$. He sells it at a discount of $$20\%$$ and still makes a profit of $$20\%$$. Find marked price.

Price of Calculator = 650

$$D = 20% of 650$$

$$ = \dfrac{1}{5} \times 650 = 130$$

Cost of Calculator after discount

$$=650-130=520$$

$$P = 20 % of 520$$

$$\begin{array}{l} =\dfrac { 1 }{ 5 } \times 520=104 \\ \\ S.P.=C.P.+P \\ \\ =520+104\Rightarrow 624 \\ \\ MP=SP+D \\ \\=624+130=754 \end{array}$$

The cost of $$18$$ chairs is $$\text{Rs.}\ 22770$$. How many such chairs can be bought for $$\text{Rs.}\ 10120$$?

Cost of $$18$$ chair$$=\text{Rs.}\ 22770$$

Cost of $$1$$ chair$$=\dfrac{22770}{18}$$

$$=1265$$

Number of chairs bought for $$\text{Rs.}\ 10120=\dfrac{10120}{1265}=8$$

Therefore, $$8$$ chairs can be bought for $$\text{Rs.}\ 10120$$

Find the discount and the selling price, when the printed price $$=$$Rs. $$12750$$, discount$$=8\dfrac{1}{3}\%$$.

$$\Pr \operatorname{int} \,\,\Pr ice\, = Rs\,12750\,,discount\,\frac{{25}}{3}\% $$

$$ \Rightarrow Then\,,\,discount\, = \frac{{25}}{3} \times \frac{{12750}}{{100}} = 1062.5\,\,rupees.$$

$$ \Rightarrow and\,\,selling\,\Pr ice\,\,is\,(12750 - discount) = 12750 - 1062.5$$

$$ = Rs11687.5\,$$

Ayesha announced a festival discount of $$25 \%$$ on all the items in her mobile phone shop. Ramandeep bought a mobile phone for himself. He got a discount of $$Rs.\ 1,960$$. What was the marked price of the mobile phone?

Suppose, the market price of the phone $$=x$$
Festival discount on phone $$=25\%$$
Ramadeep got total discount $$=Rs.\ 1960$$
As per question,
$$\Rightarrow 1960=x \times \dfrac{25}{100}$$
$$\Rightarrow 1960=\dfrac{x}{4}$$
$$\Rightarrow x=1960 \times 4=Rs.\ 7840$$

Find the discount and the discount percentage, when advertised price $$=$$ Rs. $$28500,$$ selling price $$=$$ Rs. $$24510.$$

Given: Advertised price $$= ₹\ 28500$$

Selling price $$= ₹\ 24510$$

We know that

Discount $$=$$ Advertised price $$–$$ Selling Price

$$= 28500 – 24510$$

$$= ₹\ 3990 $$

Here Discount $$\% = \bigg[\dfrac{\mathrm{Discount}}{ \mathrm{advertised\ price}} \times 100\bigg] \% $$

$$= \bigg[\dfrac{3990}{28500} \times 100\bigg] \%$$

$$= \dfrac{3990}{285} \%$$

$$=14\%$$

The marked price of a pair of jeans is $$Rs. 800$$. A customer pays $$Rs. 40$$ as tax for it. Find the rate of tax.

Price of jeans = Rs 800

Tax paid = Rs 40

Let the rate of tax be x

= x % of 800 = 40

= x/100 × 800 = 40

= x = 40 × 100 /800

= x = 40/8

= x = 5

Hence, the rate of tax is 5%

An item marked at Rs. 840 is sold for Rs.What is the discount and discount% ?

Discount = Marked price - Sale price

$$=Rs. 840-Rs. 714 = Rs. 126$$

On marked price of Rs. 840, the discount is Rs. 126.

Now,

Discount% = $$\dfrac{126}{840} \times 100=15$$%

$$CP$$ $$=$$ Rs $$400$$
$$SP$$ $$=$$ Rs $$500$$
$$Gain$$ $$%$$ $$=$$ $$?$$

We know,

$$Gain=SP-CP$$

$$Gain = 500-400\\\ \ \ \ \ \ \ \ =Rs. 100$$

Find a single discount equivalent to two successive discount of $$20\%$$ and $$10\%$$.

$$20\% $$ of $$x=0.2x$$ [Inital price =$$x]$$

New price $$=0.8x$$
$$10\%$$ of $$0.8x=0.08x$$

$$\text{New price} =(0.8-0.08)x\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =0.72x$$

Single discount equivalent $$=\dfrac{x-0.72x}{x}\times 100$$

$$=28\%$$

An item is marked at $$Rs\ 1,540$$ is sold for $$Rs\ 1,400$$ what is the discount and discount $$\%$$?

Market price $$\left(M.P\right)=Rs.1540$$

Selling price $$\left(S.P\right)=Rs.1400$$

Discount $$=M.P-S.P$$

$$=1540-1400=Rs.140$$

Discount $$\%=\dfrac{discount}{market price}\times 100=\dfrac{140}{1540}\times 100$$

$$=9.09\%$$

$$SP=1615$$
$$D=5\%$$
$$MP=?$$

We know that,

$$SP=MP-Discount\%\times MP$$

Hence, we can write

$$1615=MP-\dfrac{5}{100}\times MP\Rightarrow 1615=\dfrac{95}{100}\times MP\Rightarrow MP=\dfrac{1615*100}{95}=1700$$

$$12.5\%$$ of $$550$$ is

$$12.5\%$$ of $$550$$

$$=\dfrac{12.5}{100}\times 550=12.5\times 5.5=68.75$$

The marked price of a LCD TV is Rs.A shopkeeper allows three successive discount of $$10\%, 5\%$$ and $$2\%$$ or $$10\%$$ and a free mobile phone. Find the cost of mobile phone being offered.

$$45,400$$

After $$10\%$$ discount

$$\dfrac{90}{100}\times 45,400=40,860$$

After $$5\%$$ discount

$$\dfrac{95}{100}\times 40,860=38,817$$

After $$2\%$$ discount

$$\dfrac{98}{100}\times 38,817=38,040.66$$

$$10\%$$ discount on this price is the cost of a mobile phone.

$$\dfrac{90}{100}\times 45400=40860$$

Cost of mobile phone$$=40860-38040.66=2819.4Rs$$

The price of the mobile phone is $$Rs.2819.4$$

After giving two successive discounts, a shirt with a marked price Rs. 200 is available at Rs.If the second discount is $$20\%$$ then the first discount is

Given that, marked price of the shirt is $$Rs. \ 200$$

Also, after two successive discounts, the shirt is available at $$Rs.\ 100$$

And the second discount is $$20\%$$

Let the first discount be $$x\%$$

First discount $$\rightarrow x\%\Rightarrow \dfrac{x}{100}\times 200$$

Second discount $$\rightarrow 20\%$$ of $$\left(200-\dfrac{x}{100}\times 200\right)$$

$$\dfrac{20}{100}\times [200-2x]+\dfrac{x}{100}\times 200=100$$ [Price after both discounts is $$100$$]

$$\Rightarrow 40-\dfrac{2}{5}x+2x=100$$

$$\Rightarrow 1.6x=60$$

$$\therefore \ x=37.5$$

Hence, the first discount is $$37.5\%$$

Find the rate of discount when M.P = $$2800$$ and S.P = $$2100$$.

Given,

$$MP=2800$$

$$SP=2100$$

$$Discount=MP-SP=2800-2100=700$$

Discount Rate$$=\dfrac{Discount}{MP}\times 100\%=\dfrac{700}{2800}\times 100\%=\dfrac{100}{4}\%=25\%$$

Rate of Discount$$=25\%$$

A geometry box is marked for $$Rs.\ 325$$. If the rate of tax is $$12$$%, find the amount a customer has to pay for it.

Given:

Price marked $$=Rs.\ 325$$

Rate of tax $$=12\%$$

Tax amount $$=$$ $$12\%$$ of $$Rs.\ 325$$

$$=325\times \dfrac{12}{100}$$

$$=Rs.\ 39$$

Amount a customer has to pay $$=$$ Price marked $$+$$ Tax Amount

$$=325+39$$

$$=Rs.\ 364$$

So, a customer has to pay $$Rs.\ 364.$$

Nishant sold his scooter for Rs. 24150 making a profit of 15$$\%$$. Find the price of the scooter .

Given that,

Nishant sold his scooter for $$Rs.\ 24150$$.

He made aprofit of $$15\%$$.

To find out,

The price of the scooter.

We know that, $$CP=\cfrac { 100 }{ 100+profit\%\quad } \times SP$$

Here, $$SP=Rs.\ 24150\ and\ profit\%=15$$

$$\therefore\ CP =\cfrac { 100 }{ 100+15 } \times 24150$$

$$ =\cfrac { 100 }{ 115 } \times 24150$$

$$ =Rs.\ 21000$$

Hence, the price of the scooter is $$Rs.\ 21000$$.

The profit of selling a product is 2 times its CP if the SP is $$300$$ find CP

Let CP be x

Profit is $$2x$$

$$SP=CP+profit\\300=x+2x\\300=3x\\x=\dfrac {300}3\\x=100$$

Jaishree bought a saree for Rs. $$1456$$ at a discount of $$9$$% . Find the marked price of the saree.

1338769_1264468_ans_bbd2e29decee4ea8b625fe908bf0fdd1.jpg

An ore contains 15% of iron. How much ore will be required to get 36 kg of iron?

Content of iron in ore $$=15\%$$

$$=15$$ kg

$$\therefore 15$$kg iron in $$100$$ kg ore

$$\therefore$$ In $$36$$kg iron $$=\dfrac{100}{15}\times 36$$

$$=240$$ kg of ore.

1155514_1281963_ans_985e3dce76d24c228a7930cbcb3324e2.jpg

Anuja purchased a second hand refrigerator for rs 9800 she spent Rs 600 on its repairs and sold it at a profit of 8%. Find the selling price of the refrigerator and the amount of money she gained

Total cost price (C.P) = Rs (9800+600) = Rs 10400

profit = $$\frac{S.P-C.P}{C.P}\times 100\Rightarrow \frac{8}{100}=\frac{S.P}{C.P}-1\Rightarrow S.P=C.P(\frac{108}{100})$$

$$=\frac{10400\times 108}{100}= 11232$$ ; profit = 11232-10400= Rs 832

1181935_1293411_ans_45ac19e736e6417dad5c4ded92209d45.jpg

Mohit bought a shirt for $$Rs.\ 1337.50$$ Including $$VAT$$ at $$7\%$$ . Find the original price of the shirt.

Let $$x$$ be the original price of the shirt.

According to the question,

$$x + 7 \%$$ of $$x = 1337.50$$

$$\Rightarrow x + \cfrac{7x}{100} = 1337.5$$

$$\Rightarrow \cfrac{107x}{100} = 1337.5$$

$$\Rightarrow x = \cfrac{1337.5 \times 100}{107} $$

$$\Rightarrow x= Rs.\ 1250$$

Mr. Sawant paid $$Rs. 31,500$$ income tax then compute $$2 \%$$ education cess on it.

Mr. Sawant paid $$=Rs.31,500$$

Tax $$=21$$% of $$31,500$$

$$=\dfrac { 2 }{ 100 } \times 31500$$

$$=Rs.630$$

A geometry box is marked for Rs. $$45$$. If the rate of sales tax is $$7\%$$, find the amount a customer has to pay for it.

Marked price (M.P) of geometry box $$=$$Rs. $$45$$

Sales tax$$=7\%$$

$$=\dfrac{7}{100}\times 45$$

$$Rs=3.15$$

S.P$$=$$M.P$$+$$Sales tax

Amount customer has to pay$$=$$Rs. $$45+$$Rs. $$3.15$$

$$=$$Rs. $$48.15$$.

Dozen ball pens are bought at $$Rs250$$, on selling there is a profit of $$RS12$$. What is the $$S.P$$ of each of each ball pen?

$$\begin{array}{l} Dozen\, \, ball\, \, pens\, \, are\, \, bought\, \, at\, \, Rs.250 \\ i.e.\, \, C.P.\, \, of\, \, 12\, \, ball\, \, pen=250 \\SP.\, \, of\, \, 1\, \, ball\, \, pen=\dfrac { { 262 } }{ { 12 } } \\ =21.83\, \, \left( { approx } \right) \end{array}$$

Tim bought a box of chocolates for $$\text{Rs }650$$ and sold it to Tom at a profit of $$\text{Rs }75$$. Find the selling price.

We know that,

Given,

$$C.P.=650$$

Profit $$=75$$

$$S.P.=C.P.+$$profit

$$S.P.=650+75=725$$

Then,

We get selling price is $$\text{Rs. }725$$

Arun bought a pair of skates at a sale where the discount is given was $$20\%$$. If the amount he pays is $$Rs. 1,600,$$ then find the marked price.

The amount he paid $$=Rs.\ 1600$$

Discount $$=20\%$$

Let the $$MP$$ be $$Rs.\ x$$.

According to the question,

$$x-\dfrac{20x}{100}=1600$$

$$80x=160000$$

$$x=2000$$

$$MP = Rs.\ 2000$$

Hence, this is the answer

Convert the following ratios into percentage.
$$\dfrac {7}{16}$$

1189734_1344888_ans_a771dcff57994fda8945b0c1ae0125ea.jpg

A shopkeeper buys a suit piece for $$Rs 1,400$$ and marks it $$60\%$$ above the cost price. He allows a discount of $$15\%$$ on it. Find the market price of the suit piece and also the discount given.

C.P = Rs 1400.
M.P = 60% above the C.P.
M.P = 1400 + 60% of 1400
$$ = 1400 + \frac{60}{100} \times 1400 = 1400 + 840$$
M.P $$= Rs. 2240$$
Discount = Rate of discount $$\times$$ M.P.

$$=15\%\times2240$$

$$=3\times112$$
Discount $$ = Rs. 336$$.

Aman earn $$Rs 147$$ as interest alster $$3\ years$$ at $$7\%$$ per annum. How much did he Invest.

As simple interest $$=\dfrac{Principle \times rate \times time}{100}$$

$$\Rightarrow$$ Principle $$=\dfrac{147\times 100}{7\times 3}=$$Rs. $$700$$.

1189689_1344438_ans_6d336d430bca45d49e2d67c2cab1aa0f.jpg

The price of a sweater was slashed from $$Rs.960$$ to $$Rs.816$$ by a shopkeeper in the season. Find the rate of discount given by him.

1688707_1395970_ans_4f2869dce8dd4fac9e633fa965cd2ae7.jpg

A shopkeeper was selling all his items at $$25\%$$ discount. During the off season, he offered $$30\%$$ discount over and above the existing discount. If Pragya bought a skirt which was marked for $$Rs.\ 1200$$, how much did she pay for it?

As per question,
Market price of the skirt $$=Rs. 1200$$
During normal season discount $$@25\ \%=\dfrac{25}{100} \times 1200=Rs.\ 300$$
After the discount, price of the skirt $$1200-300$$
$$Rs.\ 900$$
In off season, the shopkeeper also offer discount $$@30\ \%=\dfrac{30}{100} \times 900=Rs.\ 270$$
Now, the price of skirt after $$30\%$$ discount,$$=900-270=Rs.\ 630$$

A tea set was bought for $$528$$ after getting a discount of $$12 \% $$ on its marked price. Find the marked price of the tea set.

1688719_1423714_ans_3836334350174f498bdc773a76936aca.jpg

Mr. anu Mishra bought a gold pendant for Rs 7208 on Dhanteras from a jewellery store advertising successive discounts of 20% and 15%. What was the marked price of the pendant?

Let the M.P. of the pendant be $$x$$

$$\therefore$$ Value of pendant after first discount $$= x-\dfrac{20}{100}\times x = \dfrac{4x}{5}$$

Now, value of pendant after second discount$$= \dfrac{4x}5-\dfrac{15}{100}\times\dfrac{4x}{5}=\dfrac{4x}5 - \dfrac{3x}{25}=\dfrac{17x}{25}$$

$$\therefore$$ Selling Price of the pendant $$=\dfrac{17x}{25}=7208$$

Solving for $$x$$ we get $$\rightarrow$$ $$x=\dfrac{7208\times25}{17}$$

$$x=10600$$

$$\therefore$$ Marked price of the pendant was $$Rs. \ 10600$$

If marked price= Rs 1700, selling price= Rs 1540 then find the discount.

$$SP=1540$$

$$CP=1700$$

Discount $$=1700-1540$$

$$=160$$Rs.

Discount $$\%=\dfrac{160}{1700}\times 100$$

$$=9.41\%$$.

1203604_1447891_ans_93a1b713ee62452e90c7b4f4ef7e8117.jpg

Railway ticket costs Rs. $$720$$. A further $$2\%$$ tax of this amount is added to it. What is the total amount of this ticket?

Given,

Cost of railway Ticket $$= x = Rs. 720$$

Tax $$= t= 2 \%$$

Total amount =$$\dfrac{720\times (100+2)}{100}$$

$$= \dfrac{720\times 102}{100}$$

$$ =Rs. 734.40 $$

Total amount of ticket $$= Rs. \ 734.40$$

What does it mean "Buy $$6$$ get $$1$$ free.""

Total Items $$= 7$$
Discounted $$= 1$$
Percentage $$=\dfrac{1}{7} \times 100= 14.285\%$$

If CP and Sp of a product are $$Rs.350, Rs.385$$ respectively. Then Find profit or loss.

CP of Product $$350Rs$$

SP of Product $$385Rs$$

Since $$SP>CP$$

It is profit.

$$ Profit =SP-CP\\P=385-350=35Rs.$$

Watson bought a book for Rs. 240 and sold to Johny at a profit of 50%. Johny wants to sell this book to Shekar so that he earns a profit of 25%. But Shekar is adamant at buying this book at a discount of 10%. What marked price should Johny quote to Shekar so as to achieve desired profit ?

1244996_1532775_ans_3c97421f31844b1a9d3dcd8cd0a6c03e.PNG

The ratio of cost price and marked price of an article is $$2:3$$ and ratio of percentage profit and percentage discount is $$3:2$$.what is the discount percentage?

CP:MP = 2x:3x

$$\Rightarrow $$ profit = MP- CP = 3x-2x=x

Profit % : discount % = 3:2

Let CP= 200, SP = 300

But $$\frac{3x}{100}\times 200+\frac{2x}{100}\times 300=6x+6x=12x$$

$$\Rightarrow 12x=100$$

$$\Rightarrow x=8.33$$%

$$\therefore $$ Discount = 2x= 16.66%

1229709_1534882_ans_7b41f10b246240569fb43f9f8947df88.PNG

Tarun got 30% concession on the labelled price of an article and sold it for Rs. 8750 with 25% profit on the price he bought. What was the labelled price ?

C.P = Rs $$(\frac{100}{125}\times 8750)= Rs 7000$$

Let the labelled price be Rs x $$\Rightarrow \frac{70x}{100}=7000$$

$$\Rightarrow x= Rs \frac{7000\times 100}{70}= Rs 10,000$$

1244964_1532228_ans_fd97a9fe084c424db18097cc05513e23.PNG

The excise duty on an article is reduced from Rs. 810 to Rs.720. Find the percentage reduction in the excise duty on that article.

1300276_1609006_ans_d106fc9dbed741c0ac1862265e7e151c.jpg

Find the S.P. if M.P. = Rs 500 and Discount = 15%

Given: $$\mathrm{M.P.} = \mathrm{Rs.} \space500$$ and $$\mathrm{Discount}\% = 15\% $$

To find: $$\mathrm{S.P.} $$

We know that $$\mathrm{S.P.}=\mathrm{M.P.}\left[\dfrac{100-\mathrm{Discount} \%}{100}\right]$$

$$\Rightarrow \mathrm{S.P.}=500\left(\dfrac{100-15}{100}\right)$$

$$\Rightarrow \mathrm{S.P.}=5 \times 85$$

$$\Rightarrow \mathrm{S.P.}=\mathrm{Rs.} \space425$$

Find the S.P. if M.P. = Rs 1300 and Discount = 10%

Given: $$\mathrm{M.P} = \mathrm{Rs.} \space1300$$ and $$\mathrm{Discount}\%$$ $$=10 \%$$

To find: $$\mathrm{S.P}$$

We know that $$\mathrm{S.P}=\mathrm{M.P}\left[\dfrac{100- \mathrm{Discount} \%}{100}\right]$$

$$\Rightarrow \mathrm{S.P}=1300\left(\dfrac{100-10}{100}\right)$$

$$\Rightarrow \mathrm{S.P}=13 \times 90$$

$$\Rightarrow \mathrm{S.P}=\mathrm{Rs.} \space1170$$

Find the M.P. if S.P. = Rs 1222 and Discount = 6%

Given: $$\mathrm{S.P}=\mathrm{Rs.} \space1222$$ and $$\mathrm{Discount}\%$$ $$=6 \%$$

To find: $$\mathrm{M.P} $$

We know that $$\mathrm{M.P}$$ $$=\mathrm{S.P}\left[\dfrac{100}{100-\mathrm{Discount} \%}\right]$$

$$\Rightarrow \mathrm{M.P}=1222\left(\dfrac{100}{100-6}\right)$$

$$\Rightarrow \mathrm{M.P}=1222 \times \dfrac{100}{94}$$

$$\Rightarrow \mathrm{M.P}=\mathrm{Rs.}\space1300$$

The marked price of a ceiling fan is RsDuring off season, it is sold for RsDetermine the discount percent.

Given, $$\mathrm{M.P}$$ of the ceiling fan $$=\mathrm{Rs}\space720$$

$$\mathrm{S.P}$$ of the ceiling fan $$=\mathrm{Rs}\space684$$

Since $$\mathrm{S.P}=\mathrm{M.P}-\mathrm{Discount}$$

$$\Rightarrow \mathrm{Discount}=\mathrm{M.P}-\mathrm{S.P}$$

$$\Rightarrow \mathrm{Discount}=720-684$$

$$\Rightarrow \mathrm{Discount}=\mathrm{Rs}\space36$$

Now, $$\mathrm{Discount}\%=\dfrac {\mathrm{Discount}}{\mathrm{M.P}} \times100$$

$$= \dfrac{36}{720} \times100$$

$$=5\%$$

After allowing a discount of $$20\%$$ on the marked price of a lamp, a trader loses $$10\%$$. By what percentage is the marked price above the cost price ?

1872146_1673777_ans_2e011b9f246c43aaa3ed5e81f8b068f5.jpeg

A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find advertised price.

1872810_1673740_ans_6dfff70c50a94ab2a2815dd39b4a1865.jpeg

On the eve of Gandhi Jayanti a saree is sold for Rs 720 after allowing 20% discount. What is its marked price ?

Given, $$\mathrm{S.P}$$ of the saree $$=\mathrm{Rs} \space720$$

Discount on the saree $$=20 \%$$

We know, $$\mathrm{Discount} \%=\dfrac{\mathrm{ Discount }}{\mathrm{MP}} \times 100$$

Or, $$\mathrm{Discount}=\dfrac{\text { Discount } \% \times \text { MP }}{100}$$

Let, the $$\mathrm{MP}$$ of the saree be $$\text{Rs. } \space x$$

$$\therefore \mathrm{Discount}=\dfrac{20}{100} x= \mathrm{Rs.} \space0.02x$$

Since, $$\mathrm{S.P}=\mathrm{M.P}-\mathrm{Discount}$$

$$720=x-0.20 x$$

$$720=0.80 x$$

$$x=\dfrac{720}{0.80}$$

$$\Rightarrow x=\mathrm{Rs} \space900$$

Thus, the $$\mathrm{M.P}$$ of the saree is $$\mathrm{Rs.} \space900$$ .

Find discount in percent when M.P. = Rs 900 and S.P = Rs 873

Given: $$\mathrm{M.P}=\mathrm{Rs.}\space900$$ and $$\mathrm{S.P}= \mathrm{Rs.} \space873$$

To find: $$\mathrm{Discount}\%$$

We know that $$\mathrm{Discount}$$ $$=\mathrm{M.P}-\mathrm{S.P}$$

$$\Rightarrow$$ $$\mathrm{Discount}= \mathrm{Rs.}\space (900-873)$$

$$\Rightarrow$$ $$\mathrm{Discount}= \mathrm{Rs.}\space 27$$

Now, $$\mathrm{Discount} \%=\frac{\text { Discount }}{\text { M.P }} \times 100$$

$$\Rightarrow$$ $$\mathrm{Discount} \%=\frac{27}{900} \times 100$$

$$\Rightarrow$$ $$\mathrm{Discount} \%=3 \%$$

A tradesman marks his goods at such a price after allowing a discount of 15%, he makes a profit of 20%. What is the marked price of an article whose cost price is Rs 170?

1872335_1673712_ans_224bfb7b938d4cc89b2dc2eb1e283dd3.jpeg

After allowing a discount of $$7\dfrac{1}{2}\%$$ on the marked price, an article is sold for RsFind its marked price.

Given, $$\mathrm{S.P}$$ of the article $$=\mathrm{Rs} \space555$$

$$\mathrm{Discount} =7.5 \%$$

Let the $$\mathrm{M.P}$$ of the article be $$\mathrm{Rs} \space x$$

$$\therefore \mathrm{Discount}=\dfrac{\mathrm{Discount} \times \mathrm{M.P}}{100}$$

$$=\mathrm{Rs} \dfrac{7.5x}{100}$$

$$=\mathrm{Rs} \space0.075x$$

Since $$\mathrm{S.P}=\mathrm{M.P}-\mathrm{Discount}$$

$$\Rightarrow555=x-0.075 x$$

$$\Rightarrow555=0.925 x$$

$$\Rightarrow x=\dfrac{555}{0.925}$$

$$\Rightarrow x=\mathrm{Rs.}\space600$$

Thus, the $$\mathrm{M.P}$$ of the article is $$\mathrm{Rs} \space600$$ .

Find the M.P. if S.P. = Rs 495 and Discount = 1%

Given: $$\mathrm{S.P} = \mathrm{Rs.} \space495$$ and $$\mathrm{Discount}\%$$ $$=1 \%$$

To find: $$\mathrm{M.P}$$

We know that $$\mathrm{M} . \mathrm{P}=\mathrm{S.P}\left[\dfrac{100}{100-\mathrm{Discount} \%}\right]$$

$$\Rightarrow \mathrm{M.P} =495\left(\dfrac{100}{100-16}\right)$$

$$\Rightarrow \mathrm{M.P}=495 \times \dfrac{100}{99}$$

$$\Rightarrow \mathrm{M.P} =\mathrm{Rs.}\space500$$

Find discount in percent when M.P. = Rs 500 and S.P. = Rs 425

Given: $$\mathrm{M.P} = \mathrm{Rs.} \space500$$ and $$\mathrm{S.P}= \mathrm{Rs.} \space425$$

To find: $$\mathrm{Discount}\%$$

We know that $$\mathrm{Discount} =\mathrm{M.P-S.P}$$

$$\Rightarrow \mathrm{Discount = Rs.}\space (500-425)$$

$$\Rightarrow \mathrm{Discount = Rs.} \space75$$

Now, $$\mathrm{Discount} \%=\dfrac{\text { Discount }}{\text { M.P }} \times 100$$

$$\Rightarrow \mathrm{Discount} \%=\dfrac{75}{500} \times 100$$

$$\Rightarrow \mathrm{Discount} \%=15 \%$$

A cycle merchant allows $$20\%$$ discount on the marked price of the cycles and still makes a profit of $$20\%$$. If he gains $$Rs. 360$$ over the sale of one cycle, find the marked price of the cycle. (in Rs.)

1520670_1673794_ans_b72dd27be67b444ea1bca8aa73b9b63a.jpg

Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of $$12.5\%$$, they make a profit of $$10\%$$. Find the marked price of a suit which costs them $$Rs. 1470$$.

1520673_1673808_ans_a79b04a9dd08448b9ec43be75c35d372.jpg

Ashish started the business with an initial investment of RsIn the first year he incurred a loss of 4%. However during the second year he earned a profit of 5% which in third year rose to 10%. Calculate the net profit for the entire period of 3 years.

Initial investment by Ashish is $$= \mathrm{Rs.}\space 500000$$

Incurred loss in the first year is $$= 4\%$$

Profit in $$\text{2nd}$$ year is $$= 5\%$$

Profit in $$\text{3rd}$$ year is $$= 10\%$$

Profit for three years$$=\mathrm{P}\left(1-\dfrac{\mathrm{R}_{1}}{100}\right)\left(1+\dfrac{\mathrm{R}_{2}}{100}\right)\left(1+\dfrac{\mathrm{R}_{3}}{100}\right)$$

$$=500,000\left(1-\dfrac{4}{100}\right)\left(1+\dfrac{5}{100}\right)\left(1+\dfrac{10}{100}\right)$$

$$=500,000(0.96)(1.05)(1.10)$$

$$=554,400$$

Thus, the net profit is $$\mathrm{Rs.}\space554,400$$

Thus, the profit = $$554,400-500,000 = Rs.\ 54,400$$

Find the rate of discount being given on a shirt whose selling price is $$1092$$ after deducting a discount of $$208$$ on its marked price. Hint: $$MP = (SP) + (discount)$$.

Given:

SP $$= ₹\ 1092$$

Discount $$= ₹\ 208$$

We know that

Market price $$=$$ SP $$+$$ Discount

$$= 1092 + 208$$

$$ = ₹1300$$

$$∴$$ The Discount % $$= \dfrac{Discount}{market\ price} \times 100 $$

$$= \dfrac{208}{1300} \times 100$$

$$ = 16\ %$$

A bookseller sells all his books at a profit of 10%. If he buys a book from the distributor at Rs 200, how much does he sell it for?

Given
Profit $$\% = 10\%$$
$$CP = Rs. 200$$
Since
$$SP = {(100 + profit\ \%)/100} × CP$$
$$= {(100 + 10)/100} × 200$$
$$= {110/100} × 200$$
$$ = Rs. 220$$

The bookseller sells the book for $$Rs. 220.$$

A business man makes a 10% profit by selling a toy costing him RsWhat is the selling price?

$$CP = \text{Rs.} 120$$
$$\text{Profit }= 10\ \%$$

We know that
$$SP = \frac{100+\text{Profit %}}{100} × CP$$
$$ =\frac{100+10}{100} × 120$$
$$ = \frac{110}{100} × 120 = 1.1 × 120 = \text{Rs.} 132$$

Given the following values, find the unknown value:
C.P = Rs 1200, S.P. = Rs 1350, Profit= ?

As it is given that $$S.P > C.P$$

$$Profit=S.P-C.P$$

$$Profit=1350-1200$$

$$Profit=Rs\ 150$$

Jyotsana bought 400 eggs at Rs 8.40 a dozen. At what price per hundred must she sell them so as to earn a profit of 15%?

Cost of eggs per dozen $$= Rs. 8.40$$
Cost of 1 egg $$= 8.40/12 = Rs. 0.7$$
Cost of 400 eggs $$= 400 × 0.7 = Rs. 280$$
Calculating the price at which Jyotsana should sell the eggs to earn a profit of $$15\%$$, we get
$$15\%\ of\ 280 + 280$$
$$= {(15/100) × 280} + 280 = {4200/100} + 280 = 42 + 280 = Rs. 322$$

So, Jyotsana must sell the 400 eggs for Rs. 322 in order to earn a profit of $$15\%.$$
Therefore, SP per one hundred eggs $$= Rs. 322/4 = Rs. 80.50.$$

Kiran purchases an article for Rs. $$5310$$ which includes $$10$$% rebate on the marked price and $$18$$% tax (under GST) on the remaining price. Find the marked price of the article.

Given:

Rate of GST $$=18$$%

CP of an article $$=x-10$$% of $$x$$

$$=x-\dfrac{10}{100}x\\=\dfrac{90x}{100}\\=\dfrac{9x}{10}$$

Amount of GST on CP on article $$=18$$% of $$\dfrac {9x}{10$}$

$$=\dfrac {18}{100}\times \dfrac {9x}{10}$$

Total CP of article $$=\dfrac {9x}{10}+\left[\dfrac {18}{100}\times \dfrac {9x}{10}\right]\\=\dfrac{9x}{10}\left(\dfrac {1+18}{100}\right)=\dfrac {118}{100}\times \dfrac{9x}{10}$$

It is given that, CP of an article including tax $$=Rs.5310$$

So,

$$\dfrac {118}{100}\times \dfrac{9x}{10}=5310$$

$$\Rightarrow x=5310\times \dfrac {100}{118}\times \dfrac{10}9=5000$$

Hence, The required marked price of an article is Rs. $$5000$$

Fill in the blanks to make the statement true.
$$30\%$$ of $$Rs.360 = .......$$

$$30\%$$ of $$Rs.360$$

$$\Rightarrow \dfrac{30}{100} \times 360$$

$$\Rightarrow Rs.108$$

$$30\%$$ of $$Rs.360 =Rs.108$$

A retailer buys a TV from a wholesaler for Rs. $$40000$$. He marks the price of the TV $$15$$% above his cost price and sells it to a consumer at $$5$$% discount on the marked price. If the sales are intra-state and the rate of GST is $$12$$%. Find:
The marked price of the TV

It is a case of intra-state transaction of goods and services
SGST=CGST$$=\cfrac{1}{2}$$GST
The marked price of the TV
It is given that , CP of TV for retailer $$=Rs.40000$$
Marked price of TV $$=Rs.40000+15$$% of $$40000$$
$$=Rs.40000+(15/100)\times 40000=Rs.40000+6000=Rs.46000$$

Fill in the blanks to make the statement true.
John sells a bat for $$Rs.75$$ and suffers a loss of $$Rs.8.$$
The cost price of the bat is .......

Selling price of bat $$= Rs.75$$

$$Loss = Rs.8$$

Hence, Cost price,

$$= 75 + 8 = 83$$

Fill in the blanks to make the statement true.
$$120\%$$ of $$50\,km = ............$$

$$120\%$$ of $$50\,km$$

$$\Rightarrow \dfrac{120}{100} \times 50$$

$$\Rightarrow 60\,km$$

$$120\%$$ of $$50\,km =60\,km$$

A green grocer had a profit of Rs. 47 on Monday, a loss of Rs. 12 on Tuesday and loss of Rs. 8 on Wednesday. Find his net profit or loss in 3 days.

Let profit be a positive integer and loss is a negative integer, because it is opposite of profit.

Then the net profit or loss in 3 days.

$$\begin{array}{l}=R s .(47-12-8) \\=Rs\ \space 27\end{array}$$

It is positive value.

Therefore, the grocer had a profit of $$Rs.\ 27$$.

_______ is a reduction on the marked price of the article.

Discount is the reduction on marked price of the article

Discount = Discount % of _____ .

Discount $$=$$ Discount $$\%$$ of Marked price

Discount = _ -

Discount is the difference between market price and selling price.

Discount $$=$$ Market price $$-$$ Selling price

Abida bought 100 pens at the rate Rs. 3.50 per pen and pays a sales tax of 4$$\%$$. The total amount paid by Abida is ______ .

Given that,

Number of pens bought by Abida $$=100$$

Cost of one pen $$=Rs. 3.50$$

She pays a sales tax of $$4\%$$.

To find out,

The total amount paid by Abida

Cost of one pen $$=Rs. 3.50$$

Hence, cost of $$100$$ pens $$=100\times 3.50$$

$$=Rs.\ 350$$

Abida also paid $$4\%$$ sales tax on $$Rs. 350$$

Therefore, the total amount paid by Abida will be:

$$350\times \dfrac {4}{100}+350\\$$

$$=350\times \dfrac {1}{25}+350\\$$

$$=14+350\\$$

$$=Rs. 364$$

Hence, the total amount paid by Abida is $$Rs.\ 364$$.

________ expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchse.

Overhead expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchse.

The marked price of an article when it is sold for Rs. 880 after a discount of 12$$\%$$ is _____ .

Given that,

The selling price of an article is $$Rs.\ 880$$.

The price is after a discount of $$12\%$$.

To find out,

The marked price of the article.

We know that, $$M.P.=\dfrac{100\times S.P.}{100-discount\%}$$

Hence, $$M.P.=\dfrac{100\times 880}{100-12}$$

$$=\dfrac{88000}{88}$$

$$=Rs.\ 1000$$

Hence, the marked price of the article is $$Rs.\ 1000$$.

Find discount in percent when M.P. $$=Rs. 625$$ and S.P. $$=562.50$$.

We know that,
$$Discount=Market \ price-selling\ price$$
And $$Discount\ \%=\dfrac{Discount}{market\ price} \times 100$$
Given, $$M.P.=Rs\ 625$$ and $$S.P.=Rs\ 562.50$$
Discount$$=625-562.50=Rs.\ 62.5$$
$$Discount\ \%=\dfrac{62.5}{625} \times 100 = \dfrac{6250}{625}= 10\%$$

The cost of a tape-recorder is $$Rs. 10,800$$ inclusive of sales tax charged at $$8\%$$. The price of the tape-recorder before sales tax was charged is _______ .

$$Rs. 10,000$$
As per question,
$$x+x\times \dfrac {8}{100}=10800$$
or $$\dfrac {108x}{100}=10800$$
or $$x=\dfrac {10800}{108}\times 100= Rs. 10000$$

The discount on an item for sale is called on the ______.

The discount on an item for sale is called on the Marked price

Arunima bought household items whose marked prices and discount $$\%$$ are as follows:
Item Quality Rate Amount Discount $$\%$$
a) Wheat flour $$1$$ packet $$200$$ $$200$$ $$16 \%$$
b) Detergent $$1$$ packet $$371$$ $$371$$ $$22.10 \%$$
c) Namkeen $$1$$ packet $$153$$ $$153$$ $$18.30\%$$

Find the total amount of the bill she has to pay.

As per question,
(a)Rate of $$1$$ packet wheat flour $$=Rs.\ 200$$
Discount $$\%=16\%$$
So, the cost price $$=Rs.(200-\dfrac{16}{100} \times 200)=Rs.\ 168$$

(b)Rate of $$1$$ packet detergent $$=Rs.\ 371$$
Discount $$\%=22.10\%$$
So, the cost price $$=Rs.(371-\dfrac{22.10}{100} \times 371)=Rs.\ 289$$

(c)Rate of $$1$$ packet namkeen $$=Rs.\ 153$$
Discount $$\%=18.30 \%$$
So, the cost price $$=Rs.(153-\dfrac{18.30}{100} \times 153)=Rs.\ 125$$

Net amount of the bill she has to pay $$=$$ price of wheat flour$$+$$ price of detergent $$+$$ price of namkeen
$$=Rs.(168+289+125)$$

$$=Rs.\ 582$$

Hence, she has to pay $$Rs.582$$

A watch worth $$Rs\ 5400$$ is offered for sale at $$Rs.\ 4,500$$. What per cent discount is offered during the sale?

Given,
Market price of watch $$=Rs.\ 5400$$
Selling price $$=Rs.\ 4500$$
We know that,
$$Discount=Market \ price-selling\ price$$
And $$Discount\ \%=\dfrac{Discount}{market\ price} \times 100$$
Now, by sing formula,
$$Discount=5400-4500=Rs.\ 900$$
$$Discount \%=\dfrac{900}{5400} \times =\dfrac{900}{54}= 16.67 \%$$

marked price

It is given that

S.P. $$= Rs. 780$$

Discount = 20$$\%$$

We know that

S.P. =$$ [1 - d/100]$$ of M.P.

Substituting the values

$$780 = \left [ 1 - \dfrac{20}{100} \right ]$$ of M.P.

By further calculation

$$780 = \dfrac{80}{100}$$ of M.P.

It can be written as

M.P. $$= 780 \times \dfrac{100}{80}$$

So we get

M.P. $$= 780 \times \dfrac{10}{8}$$

M.P. $$= \dfrac{7800}{8}$$

M.P. $$=$$ Rs.$$975$$

Therefore, the marked price of the calculator is $$Rs. 975.$$

Lemons were bought at $$Rs\ 48$$ per dozen and sold at the rate of $$Rs.40\ per\ 10$$. Find the gain or loss percent.

As per question,
Cost of one dozen lemons $$=Rs.\ 48$$
We know that, $$1$$ dozen $$=12$$ pieces.
So, cost of $$1$$ lemon $$=Rs. \dfrac{48}{12}=Rs.\ 4$$
Also $$10$$
lemons sold by $$Rs.\ 40.$$ So, Selling price of one lemon:$$=\dfrac{40}{10}=Rs.\ 4$$
Now, cost price of one lemon $$=$$ Selling price of one lemon.
So, zero profit and zero loss.

the marked price

It is given that
C.P. of a dinner set =$$ Rs.1200$$
We know that
M.P. $$= 1200 + 80 \%$$ of Rs.1200
By further calculation
$$= 1200 + \dfrac{80}{100} \times 1200$$
So we get
$$= 1200 + 80 \times 12$$
By multiplication
$$= 1200 + 960$$
$$=$$ Rs.$$2160$$

Find discount in per cent when
M.P. .$$=Rs. 900$$ and S.P. $$=Rs.\ 873$$

We know that,
$$Discount=Market \ price-selling\ price$$
And $$Discount\ \%=\dfrac{Discount}{market\ price} \times 100$$
Given, $$M.P.=Rs.\ 900$$ and $$S.P.=Rs.\ 873$$
$$Discount=900-873=Rs.\ 27$$
$$Discount\ \%=\dfrac{27}{900} \times 100 =\dfrac{27}{9}=3 \%$$

The list price of an article is $$\,450$$ and it is sold for $$\,360$$. Find the discount percent.

It is given that

M.P of an article $$= ₹\,450$$

S.P of an article $$= ₹\,360$$

Amount of discount $$= M.P – S.P$$

Substituting the values

$$= 450 – 360$$

$$= ₹\,90$$

Discount percent $$= \dfrac{discount\ times 100}{M.P}$$

Substituting the values

$$= (90 \times 100)/ 450$$

$$= 20\%$$

What percent is :
$$25$$ cm of $$4$$ metres ?

To find the percentage: $$25$$ cm of $$4$$ m

$$4$$ m $$=400$$ cm

So the percentage $$=\dfrac{25}{400}\times 100\%$$

$$=\dfrac{25}{4}\%$$

$$=6\dfrac{1}{4}\%$$

A shopkeeper buys an article for $$\,300$$. He increases its price by $$20\%$$ and then gives $$10\%$$ discount on the new price. Find the new price (marked price) of the article.

It is given that

C.P of an article $$= ₹\,300$$

Increase in price $$= 20\%$$

$$M.P = [C.P (100 + increase\,percent)]/ 100$$

Substituting the values

$$= [300 (100 + 20)]/ 100$$

So we get

$$= (300 \times 120)/ 100$$

$$= ₹\,360$$

What percent is :
40 paisa of Rs 2

we can write it as

$$ = \dfrac{40 }{ \left ( 200\times 100 \right )} $$

so we get

$$ = \dfrac{40}{200 }\times 100 % $$
Here
$$= 20\%$$

What percent is :
16 hours of 2 days ?

we can write it as
$$ = \dfrac{16} { \left ( 2\times 24 \right ) }$$
so we get
$$= \dfrac{16}{48} \times 100 \% $$
Here
$$= \dfrac{100}3 $$%
$$=33 \dfrac{1}{3}$$ %

A shopkeeper buys an article for $$\,300$$. He increases its price by $$20\%$$ and then gives $$10\%$$ discount on the new price. Find the discount given by the shopkeeper.

It is given that

C.P of an article $$= ₹\,300$$

Increase in price $$= 20\%$$

$$M.P = [C.P (100 + increase\,percent)]/ 100$$

Substituting the values

$$= [300 (100 + 20)]/ 100$$

So we get

$$= (300 \times 120)/ 100$$

$$= ₹\,360$$

Rate of discount $$= 10\%$$

Amount of discount $$= (360 \times 10)/ 100 = ₹\,36$$

A pair of shoes, marked at $$\,320$$, are sold at a discount of $$15$$ percent. Find the discount.

It is given that

M.P of shoes $$= ₹\,320$$

Rate of discount $$= 15\%$$

Amount of discount $$= (320 \times 15)/ 100 = ₹\,48$$

The list price of an article is $$\,450$$ and it is sold for $$\,360$$. Find the discount.

It is given that

M.P of an article =₹450

S.P of an article =₹360

Amount of discount = M.P – S.P

Substituting the values

=450–360

=₹90

A shopkeeper marked a dinner set for $$\, 1,000$$. He sold it at $$\,900$$. What percent discount did he give?

It is given that

M.P of a dinner set $$= ₹\,1000$$

S.P of a dinner set $$= ₹\,900$$

So the amount of discount $$= 1000 – 900 = ₹\,100$$

Discount percent $$= (Discount \times 100)/ M.P$$

Substituting the values

$$= (100 \times 100)/ 1000$$

$$= 10\%$$

Evaluate:
$$30\%$$ of $$200$$ + $$20\%$$ of $$450 25\%$$ of $$600$$

$$30\%$$ of $$200$$ + $$20\%$$ of $$450 – 25\%$$ of $$600$$

$$= (\dfrac{30 }{ 100} \times 200) + (\dfrac{20 }{ 100} \times 450) – (\dfrac{25 }{ 100} \times 600)$$

$$= (30 \times 2) + (2 \times 45) – (25 \times 6)$$

We get,

$$= 60 + 90 – 150$$

$$= 150 – 150$$

$$= 0$$

Find:
$$45$$ is what percent of $$54$$?

Let $$45=x$$ percent of $$54=\dfrac {54\times x}{100}$$

$$\Rightarrow x=\dfrac {45\times 100}{54}=\dfrac {5\times 100}{6}$$

$$=\dfrac {250}{3}=83\dfrac 13 \%$$
$$\therefore$$ Required percentage $$=83\dfrac 13 \%$$

A car is marked at $$\,50,000$$. The dealer gives $$5\%$$ discount on first $$\,20,000$$ and $$2\%$$ discount on the remaining $$\, 30,000$$. Find the total discount.

It is given that

M.P of a car $$= ₹\,50,000$$

Discount at the rate of $$5\%$$ on first $$₹\,20,000 = (20,000 \times 5)/ 100 = ₹\,1000$$

Discount at the rate of $$2\%$$ on remaining $$₹\, 30,000 = (30,000 \times 2)/ 100 = ₹\,600$$

Total discount$$= 1000 + 600 = ₹\,1600$$

Observe the table given below. Check and decide, whether the individuals have to pay income tax.

Sr. No. Individuals Age Taxable Income (Rs. ) Will have to pay income tax or not
i. Miss Nikita $$27$$ $$\text{Rs.}\ 234, 000$$ .........
ii. Mr. Kulkarni $$36$$ $$\text{Rs.}\ 327,000$$ .........
iii. Miss Mehta $$44$$ $$\text{Rs.}\ 582,000$$ .........
iv. Mr. Bajaj $$64$$ $$\text{Rs.}\ 840,000$$ .........
v. Mr. Desilva $$81$$ $$\text{Rs.}\ 450,000$$ .........
$$\text{Rs.}\ 327000$$

(i) Miss Nikita is of age $$27$$ and her taxable income is $$\text{Rs.}\ 72,34,000.$$ She doesn't need to pay income tax as her earning is less than $$\text{Rs.}\ 2,50,000.$$

(ii) Mr. Kulkarni is of age $$36$$ years and his taxable income is $$\text{Rs.}\ 3,27,000.$$ So, his taxable income falls in the slab of $$\text{Rs.}\ 2,50,001$$ to $$\text{Rs.}\ 5,00,000.$$ Thus, he needs to pay the income tax.

(iii) Miss Mehta is of age $$44$$ and has a taxable income of $$\text{Rs.}\ 5,82,000.$$ She needs to pay the income tax as her taxable income falls in the slab of $$\text{Rs.}\ 5,00,001$$ to $$\text{Rs.}\ 10,00,000.$$

(iv) Mr. Bajaj is of age $$64$$ years and has a taxable income of $$\text{Rs.}\ 8,40,000.$$ He needs to pay the income tax as his taxable income falls in the slab of $$\text{Rs.}\ 5,00,001$$ to $$\text{Rs.}\ 10,00,000.$$

(v) Mr. Desvila is of age $$81$$ years and has taxable income of $$\text{Rs.}\ 4,50,000.$$ He doesn't need to pay income tax as he is in the super senior category and has taxable income of less than $$\text{Rs.}\ 5,00,000.$$

Find:
$$2.7$$ is what percent of $$18$$?

Let $$2.7=x$$ percent of $$18=\dfrac {18\times x}{100}$$

$$\therefore x=\dfrac {2.7\times 100}{18}=\dfrac {270}{18}=\dfrac {30}{2}=15$$

$$\therefore $$ Required percentage $$=15\%$$

A shopkeeper buys an article for $$Rs. 600$$ and marks $$25$$% above the cost price. Find (i) the selling price if he sells the article at $$10$$% discount(ii) the percentage of discount if it is sold for $$Rs. 600$$.

C.P = Rs. 600 and Discount rate is 25%
$$\therefore$$ S.P = C.P + Rate of discount $$\times $$ C.P.
$$= 600 + 25% \times 600$$
$$ = 600 + \frac{25}{100} \times 600$$
$$ = 600 + 150 = Rs. 750$$
Marked price = Rs. 750
(i) Rate of discount = 10%, M.P. = Rs. 750
S.P = M.P. - discount
$$ = 750 - \frac{10}{100} \times 750$$
$$ = 750 - 75$$
$$ = Rs. 675$$
(ii) S.P = Rs. 690, M.P = 750
Discount = M.P - S.P.
$$ = 750 - 690 = Rs. 60$$
If the M.P. is $$Rs. 750$$ the discount is $$Rs. 60$$. If the M.P. is $$100$$ the discount is
$$\frac{60 \times 100}{750} = 8%$$

A dealer allows a discount of $$20$$% and still gains $$20$$%. Find the marked price of an article that costs the dealer $$Rs. 720$$.

Given: C.P.$$= Rs. 720$$,

Gain $$\%= 20\%$$

Discount $$\%= 20\%$$

Gain percentage $$=\dfrac{\mathrm {Gain}}{\mathrm{CP}}\times 100$$

$$\Rightarrow 20=\dfrac{\mathrm{Gain}}{720}\times 100$$

$$\Rightarrow \mathrm{Gain}=Rs. 144$$

And SP = CP + Gain

$$\Rightarrow $$ SP $$=720+144=Rs.864$$

Discount percentage $$=\dfrac{\mathrm{Discount}}{\mathrm {Marked\ Price}}\times 100$$

$$\Rightarrow 20=\dfrac{\mathrm{Discount}}{\mathrm {Marked\ Price}}\times 100$$

$$\Rightarrow \mathrm{Marked\ Price}=5\times \mathrm {Discount}$$

Also, Discount = Marked Price – SP

$$\Rightarrow $$ Marked Price $$–$$ Discount = SP

$$\Rightarrow $$ 5 $$\times $$ Discount $$-$$ Discount $$= ₹\ 864$$

$$\Rightarrow $$ 4 $$×$$ Discount $$= ₹\ 864$$

$$\Rightarrow $$ Discount $$= ₹\ 216$$

Marked Price $$=5\ \times$$ Discount

$$= 5 × 216 $$

$$= ₹\ 1080$$

A person purchases electronic items worth $$Rs. 2,50,000$$. The shop keeper charges him a sales tax of $$21$$% instead of $$12$$%. The purchaser does not realize that he has overpaid. But after some time he finds that he has paid excess and asks the shopkeeper to return the excess ' money. The shopkeeper refuses and the purchaser moves the consumer court. The court with due learning orders the shop-keeper to pay the purchaser the excess money paid by the way of sales tax with an interest of $$12$$% per annum. If the whole deliberation takes $$8$$ months what is the money that the purchaser gets back?

S.P = 2,50,000
Tax percent = 21%
Tax at the rate of 21%
$$ = \frac{21}{100} \times 2,50,000 = 52,000$$
$$ Rs. 52500$$
Tax at the rate of 12%
$$ = \frac{12}{100} \times 2,50,000 = 30,0000$$ $$100$$
$$ Rs. 30,000$$
Excess paid $$= 52,500 - 30,000$$
$$= Rs. 22,500$$.
Now $$P = 22,500, R = 12$$%
$$T = 8$$ months = $$\frac{8}{12}$$ years

Gas stations in the United States sell gasoline by the gallon , whereas those in Great Britain sell it by the litre. Martin heads for a trip estimating his total mileage to be 960 miles. The Great Britain pound (GBP)-U.S.dollar (USD) exchange rate is currently 1:1.52, and 1 gallon (gal) is approximately 3.785 litres (L).
The rental car firm Martin is using has a special offer: for an extra 30 GBP, Martin can lock in a subsidised fuel cost of 0.75 GBP per litre for the duration of his trip. How much approximately would Martin save with this offer? ( In USD)

2013189_478474_ans_d21a7986d1de435a95f7ed7dc380b70b.jpg

A cycle is marked at $$Rs. 3600$$ and sold for $$Rs. 3312$$. What are the discount and discount percentage?

Marked Price $$= 3600,$$ Selling Price $$= 3312$$

Discount $$= M.P – S.P$$

$$= 3600 – 3312$$

Discount$$ = Rs.288$$

Discount Percent $$=\left( \cfrac { Discount }{ M.P } \right) \times 100$$

$$=\left( \cfrac { 288 }{ 3600 } \right) \times 100$$

Percent Discount $$=8\%$$

Radhika deals with second-hand goods. She bought a second hand refrigerator for $$Rs. 5000$$. She spends $$Rs. 100$$ on transportation and $$Rs. 500$$ on its repair. She sells the refrigerator for $$Rs. 7000$$. Find the total cost price of the refrigerator.

Cost of Refrigerator $$= 5000,$$ Transport Cost $$= 100,$$ Repair Cost $$= 500$$

Selling Price $$= 7000$$

Total Cost Price $$=$$ Sum of all Costs $$= 5000 + 100 + 500 = 5600$$

Hence the total cost price is $$Rs.5600$$

Find the discount, when marked price $$=\text{Rs. }780,$$ selling price $$=\text{Rs. }721.50$$.

Discount $$=$$ Marked price $$-$$ Selling price

Given, Maked price $$=\text{Rs }780$$ and Selling price $$=\text{Rs }721.50$$

$$\implies$$ Discount $$=780-721.50=\text{Rs }58.50$$

A shopkeeper purchase a sewing machine for $$Rs.\ 1200$$. He sells it at discount of $$10$$% and still makes a profit of $$8$$%.
Find
(i) The selling price
(ii) The marked price.

$$C.P=Rs. 1200$$

Profit $$=8\%$$ of $$1200=96$$

$$i) S.P=1200+96=Rs. 1296$$

$$ii) M.P$$

Discount $$=10\%$$ of $$X=\dfrac{X}{10}$$

$$X-\dfrac{X}{10}=1296$$

$$9X=12960$$

$$X=\dfrac{12960}{9}$$

$$\therefore M.P=1440$$

	Cost (in Rs.)	Cost $$+$$ tax
$$1\ .X\ (100\ gm)$$	$$70$$	$$75$$
$$2.\ Y\ (100\ gm)$$	$$62$$	$$65$$

No.	Product	MRP (Rs)	% rebate	Amount of the rebate (Rs)	Amount to be paid (Rs)
(1)	Towel
(2)	Curtain
(3)	1 kg Biscuits

Item	Quality	Rate	Amount	Discount $$\%$$
a) Wheat flour	$$1$$ packet	$$200$$	$$200$$	$$16 \%$$
b) Detergent	$$1$$ packet	$$371$$	$$371$$	$$22.10 \%$$
c) Namkeen	$$1$$ packet	$$153$$	$$153$$	$$18.30\%$$

Sr. No.	Individuals	Age	Taxable Income (Rs. )	Will have to pay income tax or not
i.	Miss Nikita	$$27$$	$$\text{Rs.}\ 234, 000$$	.........
ii.	Mr. Kulkarni	$$36$$	$$\text{Rs.}\ 327,000$$	.........
iii.	Miss Mehta	$$44$$	$$\text{Rs.}\ 582,000$$	.........
iv.	Mr. Bajaj	$$64$$	$$\text{Rs.}\ 840,000$$	.........
v.	Mr. Desilva	$$81$$	$$\text{Rs.}\ 450,000$$	.........
			$$\text{Rs.}\ 327000$$

Comparing Quantities - Class 8 Maths - Extra Questions

Calculate $$85$$% of 9.

Calculate $$10.25$$% of $$120$$.

A dealer sells goods priced at Rs 180 after giving a discount of 25%. Find his selling price (in Rs).

Calculate $$16$$% of $$1400$$

What is 12 % of 90 ?

Calculate $$10.5$$ % of 100.

What is $$45$$% of 80?

Define discount percentage with respect to marked price.

A dress is sold at $$Rs. 550$$ after allowing a discount of $$12$$%. Find its marked price

Arun bought a pair of skates at a sale where the discount given was $$20$$%. If the amount he pays is $$Rs.\ 1,600$$, find the marked price.

Before beginning her diet, Janet weighed $$125$$ pounds. After completing the diet, she weighed $$110$$ pounds. What percent of her weight did she lose?

What percent of 20 is 30?

During a sale, a shop offered a discount of $$10$$% on the marked prices of all the items. What would a customer have to pay for one jeans marked at $$Rs. 1450$$ and two shirts marked at $$Rs. 850$$ each?

A person pays $$2,800$$ for a cooler listed at $$3,500$$. Find the discount percent offered.

Find the discount when the marked price is Rs.$$25$$ and the selling price is Rs.$$23$$.

Find: $$0.6\ \%\ of\ 45=\dfrac{m}{100}$$. Find $$m$$

Find $$32 \%\ of\ 425$$

Ankit bought a pair of shoes at a discount of $$30\%$$. If he paid Rs. $$1,250$$, find the marked price.

Find the gain or loss:C.P. $$=$$Rs. $$3.50$$; S.P. $$=$$Rs. $$4.25$$.

Find the gain or loss.C.P. $$=$$Rs. $$112.25$$; S.P. $$=$$Rs. $$131.00$$.

The cost of a pair of roller skates at a shop was Rs.The sales tax charged was 5%. Find the bill amount.

Find the discount and the amount paid annually if a shirt having a price tag of $$600$$ is $$15$$% discount.

Krishnamurti bought oranges at $$Rs. 5$$ a dozen. He had to sell them at a loss of $$4%$$. Find the selling price of each orange.

Solve:$$31\% \,of\,40$$

A person has money to buy $$25$$ cycles worth Rs. $$500$$ each. How many cycles he will be able to buy if each cycle is costing Rs. $$125$$ more?

If the cost of $$7\ m$$ of cloth is $$Rs. 1470$$, find the cost of $$5\ m$$ of clothe.

If the $$S.P$$ is greater than the $$C.P$$ there is____________

If $$M.P=x$$ and $$S.P=y$$, then $$d$$%=?

Kirti bookstore sold books worth Rs.$$2,85,891$$ in the first week of june and books worth Rs.$$4,00,768$$ in the second week of the month.How much was the sale for the two weeks together?In which week was the sale greater and by how much?

The SP of a product is $$480$$ and Loss is $$30$$ find CP

A shop keeper bought a bicycle for $$Rs.3000$$ and sold the same for $$Rs.3400$$. How much was his profit?

Express the following precentages as ratios in the reduced form.$$0.64\%$$

$$40\%$$ of $$250$$

Find the value of x if$$8\%$$ of Rs.x is $$Rs.100$$

What is $$15\%$$ of $$20$$ ?

Simplify:$$15\%$$ of $$920$$

Find the cost price, if : $$S.P. =Rs.\,340$$ and gain $$= Rs.\,20$$

Find the value of x if$$45\%$$ of marks x is $$405.$$

Find the value of x if$$32\%$$ of $$x \,kg$$ is $$400\,kg$$

Find the cost price, if : $$S. P. = Rs.\,200$$ and $$loss = Rs.\,50$$

Sachin and Sanjana are calculating $$23\%$$ of $$800.$$Now calculate $$52\%$$ of $$700$$ using both the ways described above. Which way do you find easier ?

______ is charged on the sale of an item by the government and to the bill amount.

Sale tax $$= 5 \%$$ of ________.

What is $$100\%$$ of $$500$$ ?

Jyosana bought a product for $$Rs. \ 3,155$$ including $$4.5 \%$$ sales tax. Find the price before tax was added.

Music $$CD$$ originally priced at $$Rs\ 120$$ is on sale for $$25\%$$ off. What is the $$S.P.$$ ?Sonia and Rahil have different ways of calculating the sale price for the items they bought.As you work on the next problem, try both of these methods to see which you prefer.

What is $$800\%$$ of $$800$$ ?

Find out $$8\%$$ of $$25\,kg.$$

Write as a percentage :$$1.63$$

At a toy shop price of all the toys is reduced to $$66\%$$ of the original price.What is the sale price of a toy that originally costs $$Rs\ 90$$?

The table shows the cost of sunscreen of two brands with the without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate each brand.Cost (in Rs.)Cost $$+$$ tax$$1\ .X\ (100\ gm)$$$$70$$$$75$$$$2.\ Y\ (100\ gm)$$$$62$$$$65$$

Mohit sold a T.V. for Rs. $$3,600$$, gaining one-sixth of its selling price. Find the gain (in Rs.)

An article marked at $$Rs. 1000$$ is sold at a discount of $$20\%.$$. Find selling price of the article in $$Rs.$$

A dealer is selling an article at a discount of $$5$$ $$\%$$ on the marked price and its marked price is Rs. $$140$$. What is the cost price, if the marked price is $$12\%$$ above the cost price?

An article marked at Rs. 450 is sold at a discount of 20%. Find the selling price of the article.

An article marked at Rs. 450 is sold at a discount of 20%. Find the discount on the article.

A shopkeeper allows $$10 \%$$ discount on his article. What price must he mark on an article, which costs him $$Rs. \ 750$$, to make a profit of $$20 \% $$?

A trader gives $$25 \%$$ discount on his articles and still makes a profit of $$25 \%$$. Find his profit per cent, if he sells his articles at $$10 \%$$ discount.

A firm, dealing in furniture, allows $$4\%$$ discount on the marked price of each item. What price must be marked on a dining table which costs Rs.$$400$$ to assemble, so as to make a profit of $$20\%$$?

Find which of the following discount series is better for the customer :$$(i) 30\%, 20\%,$$ and $$10\%; \\$$$$(ii) 25\%, 20\%,$$ and $$15\%.$$

A shopkeeper allows two successive discounts of $$10\%$$ and $$15\%$$ on his articles. If he gets Rs. $$459$$ for an article, find its marked price.

The list price of a watch is Rs.A customer gets two successive discounts, the first being 10%. Calculate, in percentage, the second discount, if the customer pays Rs 306 for it.

Govind & Murari started a business with equal capitals. Govind terminated the partnership after 7 months. At the end of the year they earned a profit of RsFind the difference in each profit

A wholesaler allows a discount of 20% on the list price to a retailer who sells it at 5% discount on the list price. If a customer paid Rs. 114 for an article, what profit is made by the retailer? Find, also the retailer's percentage profit on his cost.

A dealer is selling an article at a discount of $$5\%$$ on the marked price. What is the selling price, if the marked price is Rs. $$140$$?

A shopkeeper allows $$20\%$$ discount on the advertised prices of his goods and still makes a profit of $$12\%$$ on his cost price. Calculate the advertised price of an article on which gains Rs. $$135$$.

David started a business establishment by investing Rs.After 4 months William entered into a partnership by investing a certain amount. At the end of the year, the profit was shared in the ratio 9 :Find how much money was invested by William.

Find discount in percent when M.P.=Rs.500 and S.P.=Rs.425

Find discount in percent when M.P.= Rs.900 and S.P.=Rs.873

Fins a single discount equivalent (in $$\%$$) to the discount series $$25\%, 20\%$$ and $$10\%$$

The marked price of a woolen coat is RsIt is sold at a discount of $$15 \%$$ The shopkeeper has allowed a further discount of 5% due to off season Find the selling price (in Rs) of the coat

A man buys an article and sells it at a profit of $$20$$%. If he would buy it at $$20$$% less and sell it for Rs $$75$$ less he would have gained $$25$$%. What is the cost price (in Rs) of the article?

Tanoj & Manoj started a business by investing Rs 75000 and Rs 90000 respectively. It was decided to pay Tanoj a monthly salary of Rs 1875 as he was the active partner. At the end of the year if the total profit is Rs 39000 find the difference of their profits

Nitesh & Jitesh invested Rs 15000 and Rs 18000 respectively in a business. If the total profit at the end of the year is Rs 8800 and Nitesh being an active partner gets an additional 12.5% of the profit, find the total profit of Nitesh in Rs

David started a business establishment by investing RsAfter 4 months William entered into a partnership by investing a certain amount. At the end of the year the profit was shared in the ratio 9 :Find how much money was invested by william in Rs

M: The price of T.V. set inclusive of Sales Tax of 9% is Rs. 13,Find its marked price. A: If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?Then M+A is

The marked price of two articles A and B together is $$\text{Rs. } 6,000$$. The sales tax on article A is $$8\%$$ and that on article B is $$10\%.$$ If on selling both the articles, the total sales tax collected is $$\text{Rs. } 552,$$ find the marked prices of each of the articles A and B.

Increases to 15%

A person bought an article and sold it at a loss of 15%. If he bought it for 20% less and sold it for Rs. 114 more he would have had profit of 30% . Find the cost price of the article.

Find the gain or loss:
C.P. $$=$$Rs. $$3.50$$; S.P. $$=$$Rs. $$4.25$$.

Find the gain or loss.
C.P. $$=$$Rs. $$112.25$$; S.P. $$=$$Rs. $$131.00$$.

Solve:
$$31\% \,of\,40$$

Express the following precentages as ratios in the reduced form.
$$0.64\%$$

Find the value of x if
$$8\%$$ of Rs.x is $$Rs.100$$

Find the cost price, if :
$$S.P. =Rs.\,340$$ and gain $$= Rs.\,20$$

Find the value of x if
$$45\%$$ of marks x is $$405.$$

Find the value of x if
$$32\%$$ of $$x \,kg$$ is $$400\,kg$$

Find the cost price, if :
$$S. P. = Rs.\,200$$ and $$loss = Rs.\,50$$

Sachin and Sanjana are calculating $$23\%$$ of $$800.$$
Now calculate $$52\%$$ of $$700$$ using both the ways described above. Which way do you find easier ?

Music $$CD$$ originally priced at $$Rs\ 120$$ is on sale for $$25\%$$ off. What is the $$S.P.$$ ?
Sonia and Rahil have different ways of calculating the sale price for the items they bought.
As you work on the next problem, try both of these methods to see which you prefer.

Write as a percentage :
$$1.63$$

At a toy shop price of all the toys is reduced to $$66\%$$ of the original price.
What is the sale price of a toy that originally costs $$Rs\ 90$$?

The table shows the cost of sunscreen of two brands with the without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate each brand.
Cost (in Rs.) Cost $$+$$ tax
$$1\ .X\ (100\ gm)$$ $$70$$ $$75$$
$$2.\ Y\ (100\ gm)$$ $$62$$ $$65$$

Find which of the following discount series is better for the customer :
$$(i) 30\%, 20\%,$$ and $$10\%; \\$$
$$(ii) 25\%, 20\%,$$ and $$15\%.$$

M: The price of T.V. set inclusive of Sales Tax of 9% is Rs. 13,Find its marked price.
A: If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V.?

Then M+A is

A shopkeeper bought an article for Rs. $$3,450$$. He marks the price of the article $$16\%$$ above the cost price. The rate of sales tax charged on the article is $$10\%$$. Find the :
(i) marked price of the article
(ii) price paid by a customer who buys the article.

Suresh purchased the following articles from Swarah Khadi Bhandar. The rebate on each article is $$20$$%. Find the total amount he paid at the time of purchase.
$$2$$ towels for $$Rs. 90$$ each
$$3$$ shirts for $$Rs. 220$$ each
$$4$$ trousers for $$Rs. 290$$ each

Calculate and fill the table on the basis of the details given below:
No. Product MRP (Rs) % rebate Amount of the rebate (Rs) Amount to be paid (Rs)
(1) Towel
(2) Curtain
(3) 1 kg Biscuits

Find the gain or loss.
C.P. $$=$$Rs. $$435.00$$; S.P. $$=$$ Rs. $$565.00$$.

A shop gives $$20\%$$ discount. What would the price of each of these be?
A dress market at $$Rs.120$$
A pair of shoes market at $$Rs.750$$
A bag market at $$Rs.250$$

$$CP$$ $$=$$ Rs $$400$$
$$SP$$ $$=$$ Rs $$500$$
$$Gain$$ $$%$$ $$=$$ $$?$$

$$SP=1615$$
$$D=5\%$$
$$MP=?$$