Comparing Quantities - Class 7 Maths - Extra Questions

Express each of the following as a ratio:
$$7.5\%$$

Percentage can be expressed as a ratio with its second term $$100$$ and first term equal to the given percentage.
We have
$$(7.5/100)$$
$$=(75/1000)$$
$$=3/40$$
$$=3:40$$


Express $$16\dfrac{2}{3}\%$$ as a ratio in the lowest form.

$$\Rightarrow 16\dfrac{2}{3}\% = \dfrac{50}{3}\% = \dfrac{50}{3} \times \dfrac{1}{100}$$
$$= \dfrac{1}{6}$$ i.e. $$1 : 6$$


Express $$\dfrac{1}{6}$$ as a per cent.

$$\Rightarrow \dfrac{1}{6} = \dfrac{1 \times 100}{6 \times 100} = \dfrac{100}{6} \%$$
$$= \dfrac{50}{3} \% = 16.66\%$$


Express $$80\%$$ as fraction in its lowest term.

$$80\% = \dfrac{80}{100} $$

          $$= \dfrac{4}{5}$$


Express $$\dfrac{9}{40}$$ as a per cent.

$$\Rightarrow \dfrac{9}{40} = \dfrac{9}{40} \times {100} = 22.5% $$




Convert each of the following fractions into a percentage:
$$(47/100)$$

In order to convert a fraction into a percentage multiply the fraction by $$100$$ and put the percent sign $$\%$$
$$=(47/100)\times 100$$
$$=47\%$$


Express the following fractions as a percent:
$$\dfrac {3}{200}$$

$$3 / 200$$

Fractions as percentage is shown below

$$\dfrac3 { 200} \times 100 = 3 / 2$$

We get,

$$= 1.5\%$$



Express the following fractions as a percentage:
$$\dfrac{7}{6}$$

$$\dfrac{7}{6} = \dfrac{7 \times 100}{6}\% =116.6\%$$


Express the following fractions as a percentage:
$$\dfrac{13}{40}$$

$$\dfrac{13}{40} = \dfrac{13 \times 100}{40}\% = 32.5\%$$


Express the following percentages as a decimal :
$$122\%$$

$$122\% = \dfrac{122}{100} = 1.22$$


Fill in the blanks:
$$135\%$$ converted to decimal is .......

$$135\%$$ converted to decimal is .......
$$135\% = \dfrac{135}{100} = 1.35$$


Express the following fractions as a percent: 
$$65 / 80$$

$$65 / 80$$

Fractions as percentage is shown below

$$\dfrac{65 }{ 80} \times 100 =\dfrac{65 } 8 \times 10$$

$$= 325 / 4$$

On further calculation, we get

$$=81.25\%$$



Express the following fraction as a percent: 
$$\dfrac{5 }{ 6}$$

Given: $$5 / 6$$

Fraction as a percentage is shown below:

$$\dfrac5  6 \times 100 = 500 / 6$$

On calculating, we get

$$=83.33\%$$



Convert $$\dfrac{5}{16}$$ into percentages.

Given: $$\dfrac{5}{16}=>\dfrac{5}{16}*100$$%

$$=\dfrac{500}{16}$$%

$$=31.25$$%


By selling a certain number of goods for Rs. $$5,500$$, a shopkeeper loses equal to one-tenth of their selling price. Find the loss.

Given, $$ S.P. = Rs  5500 $$ 

Now as per given condition

$$ Loss = \dfrac {5500}{10}  = Rs 550 $$


A person buys 12 eggs for Rs 15 and sells them at 10 for Rswhat does he gain or lose percent ?

Cost price per egg $$= \frac{15}{12} = Rs. 1.25$$
Selling price per egg $$=\frac{ 14}{10} = RS. 1.40$$
S.P>C.P
$$\therefore Gain  = 1.40 - 1.25 =Rs. 0.15$$
gain%$$  = \frac{.15}{1.25}\times 100=12$$%


A student buys a pen for Rs 90 and sells it for RsFind his gain and gain percent.

For student :
Cost price of pen$$=Rs. \ 90$$

Selling price of pen$$=Rs.\ 100$$

Since, $$SP>CP.$$

Hence, 
$$Gain=SP-CP=100-90=Rs.\ 10$$

So,
$$Gain(\%)=\dfrac{gain}{CP}\times 100=\dfrac{10}{90}\times 100=11\dfrac{1}{9}$$


Convert the given fractional numbers to percentage:
$$\cfrac{1}{8}$$

$$\cfrac{1}{8}=\cfrac{1}{8}\times 100$$%  $$=\cfrac{25}{2}$$%$$=12.5$$%


Write given ratio as percent $$ \dfrac{7}{125} $$ 


1682992_1673563_ans_225b4b5c791942b1bc9904f974c013a5.jpg


Express the following ratio as percentages:
93 : 80

$$ 93 : 80$$
It can be written as 
$$93 : 80 = 93/80$$
By further calculation
= $$ 93/80 \times 100%$$
So we get
= $$ 93/4 \times 5%$$
= $$465/4$$ %
= $$116.25$$ %


Express the following fractions as percentages:
(i) 3/2

 $$3/2$$
It can be written as
= $$3/2 \times 100%$$
$$= 150$$%


Express the following ratio as percentages:
13 : 18

 $$13 : 18$$
It can be written as 
$$13 : 18 = 13/18$$
By further calculation
= $$ 13/18 \times 100%$$
So we get
= $$ 13/9 \times 50%$$
= $$650/9 $$%
= $$72  2/9 $$%


Express :
$$3\dfrac25$$ as percent  

We can write it as 
$$3\dfrac25$$ $$ =  \left ( 3 \times 5 + 2 \right ) 5 = 17/5$$ 
By converting 17/5 as a percent 
$$ 17/5 \times 100 $$
= 340 %


Express each of the following per cents as decimals: $$0.05\%$$

$$0.05$$%
$$=0.05\times \dfrac{1}{100}$$
$$=\dfrac{0.05}{100}$$
$$=0.0005$$


Express each of the following fractions as a per cent:$$ \dfrac{53}{100} $$

$$\dfrac{53}{100}$$
$$=53\ {\dfrac{1}{100}}$$
$$=53$$%


Express $$\dfrac{1}{100}$$ as a per cent.

$$\Rightarrow \dfrac{1}{100} = 1\%$$


Express $$150\%$$ as a ratio in the lowest form.

Given, 
$$= 150\% $$

$$= \dfrac{150}{100} $$

$$= \dfrac{3}{2}$$ 

i.e. $$3 : 2$$


Write $$\dfrac { 3 }{ 20 } $$ as percentage.

$$\cfrac { 3 }{ 20 } \times 100$$% $$=3\times 5$$% $$=15$$%


Express $$\dfrac { 2 }{ 5 } $$ as percentage.

$$=\cfrac { 2 }{ 5 } \times 100$$%
$$=\cfrac { 2 }{ 5 } \times 100=40$$%


Write $$\dfrac { 4 }{ 25 } $$ as percentage.

$$\cfrac { 4 }{ 25 } \times 100$$% $$=4\times 4=16$$%


Write $$\dfrac { 36 }{ 50 } $$ as percentage.

$$\cfrac { 36 }{ 50 } \times 100$$% $$=36\times 2$$% $$=72$$%


Write given ratio as percent $$11:80$$


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Write given ratio as percent $$3:25$$


1682798_1673541_ans_62bed02a29144595b46cd9ea2f07a9f3.jpg


Write each of the following as percent : $$ \dfrac{7}{25} $$ 


1682766_1673522_ans_9a90bb396c084d9da48b2d494d8012ba.jpg


Rajiv bought a horse for Rs. $$20000$$ and sold it for Rs. $$25000$$ . Check if Rajiv made profit or loss in this transaction. Find the profit or loss per cent.

cost price of horse = Rs.$$20000 $$

selling price = Rs.$$25000$$

 profit % = $$\dfrac{SP-CP}{CP}\times 100=\dfrac{25000-20000}{20000}\times 100$$ 

                =$$25\%$$ 

since $$\dfrac{SP-CP}{CP}$$ is positive. 

Rajiv made a profit of $$25$$%


A coal merchant makes a profit of $$20 \%$$ by selling firewood at $$Rs. \ 25 $$ per quintal. Find the profit if he sells the firewood at $$Rs. \ 22.50$$

Lets cots price of coal is Rs X per Qu
then profit  per Qu=25-X
so
as per question profit on one Qu coal is Rs20%
so $$\cfrac {25 - X}{X} = \cfrac{20}{100}$$
$$ X = \cfrac {125}{6}$$
Then cost of $$240$$ Qu coal = $$ 240 \times \cfrac{125}{6} = 5000$$
Then as per question S.P of $$240$$ Qu coal = $$240\times 22.5=5400$$
so profit =$$5400-5000=400$$
Then $$\%$$ of profit =$$400\times \frac{100}{5000}$$=$$8 \%$$


$$\displaystyle \frac{5}{16}$$ in percentage form is 31.25%, if this statement is true then enter $$1$$ and if false then enter $$0$$.

Given fraction is $$ = \dfrac {5}{16} $$

Converting it to percentage, $$ \dfrac {5}{16} \times 100 = \dfrac{5}{4}\times 25 = 31.25 \% $$

Hence, the statement is true.




Express $$4\dfrac{1}{8}$$ as percent

$$4 \dfrac{1}{8} = \dfrac{33}{8} = \dfrac{33}{8} \times 100$$ % = $$412.5$$ %


$$\dfrac{24}{8}$$ can be expressed in percentage as $$\_\_\_\%$$.

$$\dfrac{24}{8}$$ can be expressed in percentage as
$$\dfrac{24}{8}\times100\%=(24 \div 8)\times 100 \%= 300 \%$$


Express $$\dfrac{1000}{10}$$ in percentage.

To convert a fraction to a percent, rewrite the fraction with a denominator of $$100$$:
$$\dfrac{1000}{10}=\dfrac{10000}{100}=10,000\%$$


If cost price $$=$$ Rs. $$100$$, selling price $$=$$ Rs. $$120$$, then find the profit

We have, C.P. $$=$$ Rs. $$100$$ and S.P. $$=$$ Rs. $$120$$
Profit $$=$$ Selling price $$-$$ Cost price
$$= 120 - 100 =$$ Rs. $$20$$
Therefore, profit $$=$$ Rs. $$20$$


Write following fraction as percentage: 
$$\dfrac{9}{25}$$

$$\dfrac{9}{25} = \dfrac{9}{25} \times 100 = 36$$ %


What $$\%$$ the fraction represents:
$$\frac{47}{50} \times \frac{100}{100}$$

$$\dfrac{47}{50}\times \dfrac{100}{100}$$

To convert this to percentage, multiply by $$100$$

i.e., $$\dfrac{47}{50}\times \dfrac{100}{100}\times\dfrac{1}{100} \%$$

$$=\dfrac{47}{50}\times\dfrac{1}{100} \ \%$$

$$=0.94\times 100 \ \%$$

$$=94 \ \%$$



Convert the following fraction into percents $$=\dfrac{1}{8}$$

$$\cfrac{1}{8}=\cfrac{100}{8\times100}\\\ \ \ \ =\cfrac{100}{8}\%\\ \ \ \ \ \ =12.5\%$$


Convert the following percentage into fraction in simplest form:
$$25\%$$

$$25\%=\cfrac{25}{100}=\cfrac{1}{4}$$



Find the gain or loss.
C.P. $$=$$ Rs. $$550.75$$; S.P. $$=$$ Rs. $$475.30$$.

we are given,
C.P. = Rs 550.75 & S.P. = Rs 475.30 
So, S.P - C.P. = 475.30 - 550.75 
$$ = -75.45 < 0$$
$$ \therefore S.P -C.P < 0 $$
$$ \therefore S.P < C.P.$$
We loss.

1181895_1069032_ans_98bb9e1c00f2414087ade4c6173ca907.jpg


Find the gain or loss percent when:
CP$$=Rs.2400$$ and SP$$=Rs.2592$$

We have,
Cost Price, $$CP = Rs. 2400$$
Selling Price, $$SP = Rs. 2592$$

We know that if the selling price is greater than cost price, then seller have a profit or gain.

Therefore,
Gain $$\%=\dfrac{SP-CP}{CP}\times 100$$
Gain $$\% = \dfrac{2592-2400}{2400} \times 100 $$
Gain $$\%=\dfrac{192}{24}$$
Gain$$\% = 8\%$$

Hence, the gain is $$8\%.$$


Express the following fractions as a percentage.
(a) $$\dfrac{3}{4}$$

(b) $$\dfrac{4}{20}$$

(c) $$\dfrac{1}{2}$$

(d) $$\dfrac{2}{3}$$

(e) $$\dfrac{3}{5}$$

(f) $$2\dfrac{1}{7}$$

(g) $$\dfrac{1}{5}$$

(h) $$\dfrac{4}{15}$$

(i) $$\dfrac{1}{6}$$

(j) $$4\dfrac{3}{8}$$

(k) $$\dfrac{8}{9}$$

(l) $$1\dfrac{1}{9}$$

Percentages of the given fractions are below

  $$ \left( a \right)\,\,\,\dfrac{3}{4}=\dfrac{3}{4}\times 100=75 $$%

 $$ \left( b \right)\,\,\,\dfrac{4}{20}=\dfrac{1}{4}=\dfrac{1}{4}\times 100=25 $$%

 $$ \left( c \right)\,\,\,\dfrac{1}{2}=\dfrac{1}{2}\times 100=50 $$%

 $$ \left( d \right)\,\,\dfrac{2}{3}\,=\dfrac{2}{3}\times 100=66.667 $$%

 $$ \left( e \right)\,\,\,\dfrac{3}{5}=\dfrac{3}{5}\times 100=60 $$%

 $$ \left( f \right)\,\,2\dfrac{1}{7}=\dfrac{15}{7}=\dfrac{15}{7}\times 100=214.286%$$%

 $$ \left( g \right)\,\,\dfrac{1}{5}=\dfrac{1}{5}\times 100=20 $$%

 $$ \left( h \right)\,\,\dfrac{4}{15}=\dfrac{4}{15}\times 100=26.67 $$%

 $$ \left( i \right)\,\,\dfrac{1}{6}=\dfrac{1}{6}\times 100=16.667 $$%

 $$ \left( j \right)\,\,4\dfrac{3}{8}=\dfrac{35}{8}=\dfrac{35}{8}\times 100=\dfrac{3500}{8}=437.5 $$%

 $$ \left( k \right)\,\,\dfrac{8}{9}=\dfrac{8}{9}\times 100=\dfrac{800}{9}=88.89%$$%

 $$ \left( l \right)\,\,1\dfrac{1}{9}=\dfrac{10}{9}=\dfrac{10}{9}\times 100=\dfrac{1000}{9}=111.111 $$%




Express the following as percentages
$$\frac{126}{1050}\times 100$$

$$\cfrac{126}{1050}\times 100=12\%$$


 Express each of the following as a fraction: 
i. $$48\,\% $$
ii.$$ 220\,\% $$

We know the number has to be divided by 100 we get,

i. $$48\,\% = 48/100 = 12/25$$ 
ii. $$220\,\% = 220/100 = 11/5 $$



Convert the given fractional numbers to per cents.
  1. $$\dfrac{1}{8}$$
  2. $$\dfrac{5}{4}$$
  3. $$\dfrac{3}{40}$$
  4. $$\dfrac{2}{7}$$

$$(1)$$ $$\cfrac{1}{8}=\cfrac{1}{8}\times 100=12.5\%$$
$$(2)$$ $$\cfrac{5}{4}=\cfrac{5}{4}\times 100=125\%$$
$$(3)$$ $$\cfrac{3}{40}=\cfrac{3}{40}\times 100=7.5\%$$
$$(4)$$ $$\cfrac{2}{7}=\cfrac{2}{7}\times 100=28.57\%$$


Tell what is the profit or loss in the following transactions . Also find profit percent or loss percent in each case.
(a) gardening shears bought for INR $$250$$ and sold for INR $$325$$.

As the cost price is less than the selling price, it is a profit.
Profit = S.P. - C.P. = Rs. 325 - Rs. 250 = Rs. 75
Profit percent = $$\dfrac{\text{Profit}}{\text{C.P.}} \times 100\%=\dfrac{75}{250}\times100\%=30\%$$


Convert the following fraction into percentage:
$$\cfrac{546}{600}$$

Given ratio is  $$ \dfrac{546}{600} $$

In terms of percentage

$$ \dfrac{546}{600}\times 100 = 91\% $$
 


What percent is equivalent to $$\cfrac{3}{8}$$?

$$\frac{3}{8}\times100=0.375\times100=37.5\%$$


Convert to percent
$$\cfrac{33\cfrac{1}{3}}{100}$$

$$\longrightarrow \dfrac{33\dfrac{1}{3}}{100}=\dfrac{\left(\dfrac{100}{3}\right)}{100}=\dfrac{100}{3\times 100}=\dfrac{1}{3}$$
Percentage $$=\dfrac{1}{3}\times 100=33.33\%$$


Express the following percentage as a fraction 
 $$47\%$$

$$47\%$$
$$=\dfrac{47}{100}$$
Hence, this is the answer.


Convert the following to percents:
$$\dfrac {12}{16}$$

To convert a fraction into %, multiply it by 100.
Therefore, ( 12 / 16 ) x 100
                 = 0.75 x 100
                 = 75%


Convert the following into percentage :
$$\dfrac{9}{20}$$

To convert it into $$\%$$.
Multiply the fraction by $$100.$$
Thus,
in $$\% = ( \dfrac{9}{20}) \times 100$$
$$ = ( 0.45) \times  100$$
$$ =  45\%$$

Hence, this is the answer.


Convert the following into percentage :
$$\dfrac{5}{12}$$

To convert it into $$\%$$.
Multiply the fraction by $$100.$$
Thus,
in $$\% = ( \dfrac{5}{12}) \times 100$$
$$ = ( 0.41666) \times  100$$
$$ =  41.666 \%$$

Hence, this is the answer.


Prachi bought a bangle box for Rs.She sold it for Rs. 425.  Find her profit percent.

Cost price of bangle box = 350 Rs
selling price of bangle box = 425 Rs
Profit = SP-CP= 425-350
profit = 75 Rs
now profit % = $$\frac{profit}{CP}\times 100=\frac{75}{350}\times 100$$
profit % = 2.14%

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Express the fraction as percentage $$\dfrac {3}{100}$$.

Fraction as percentage

$$\dfrac{3}{100} = 0.03 = 3\%$$


Find the gain or loss percent if C.P$$=$$Rs$$200$$ and S.P$$=$$Rs.$$224$$

C.P.$$=$$Rs.$$200$$ and S.P.$$=$$Rs.$$224$$
$$\therefore$$ Gain $$=$$ S.P. $$-$$ C.P.
$$=$$ Rs. $$224 –$$ Rs $$200$$
$$=$$ Rs. $$24$$
Gain $$\% = \dfrac{\left(gain\times 100\right)}{C.P}$$.
$$= \dfrac{\left(24 \times 100\right)}{200}$$
$$=12\%$$


Express the fraction as percentage $$\dfrac {29}{100}$$.

We have,
$$\dfrac{29}{100}=29\%$$.


Express the fraction as percentage $$\dfrac {151}{100}$$.

Fraction as percentage
$$\dfrac{151}{100} = 1.51 = 151\%$$


Convert given percents to decimal fractions and also to fractions in simplest forms:
$$20$$%

Percent $$=20$$%
Fractions $$=\cfrac{20}{100}$$
Simplest form $$=\cfrac{1}{5}$$
Decimal form $$=0.2$$


Convert given percents to decimal fractions and also to fractions in simplest forms:
$$150$$%

Percents $$=150$$%
Fractions $$=\cfrac{150}{100}$$
Simplest form $$=\cfrac{3}{2}$$
Decimal form $$=1.5$$


Convert given percents to decimal fractions and also to fractions in simplest forms:
$$25$$%

Percents $$25$$%
Fractions $$=\cfrac{25}{100}$$
Simplest form $$=\cfrac{1}{4}$$
Decimal form $$=0.25$$


Convert given percents to decimal fractions and also to fractions in simplest forms:
$$5$$%

Percent $$=5$$%
Fractions $$=\cfrac{5}{100}$$
Simplest form $$=\cfrac{1}{20}$$
Decimal form $$=0.05$$


Convert the given fractional numbers to percent:
$$\cfrac{2}{7}$$

$$\cfrac{2}{7}=\cfrac{2}{7}\times 100$$% $$=\cfrac{200}{7}$$%$$=28\cfrac{4}{7}$$%


Write each of the following as percent : $$ \dfrac{14}{625} $$


1682755_1673527_ans_bff99c7484d845da93460b5bbf375c1e.jpg


Convert the given fractional numbers to percent:
$$\cfrac{3}{40}$$

$$\cfrac{3}{40}=\cfrac{3}{40}\times 100$$%$$=\cfrac{3}{2}\times 5$$%$$=\cfrac{15}{2}$$% $$=7.5$$%


Convert the given fractional numbers to percent:
$$\cfrac{5}{4}$$

$$\cfrac{5}{4}=\cfrac{5}{4}\times 100$$%  $$=5\times{25}$$%$$=125$$%


Express each of the following per cents as decimals: $$75\%$$

$$75$$%
$$=75 \times \dfrac{1}{100}$$
$$=\dfrac{75}{100}$$
$$=0.75$$


Express  $$125\,\%$$ as a ratio: 

By dividing the given number we get,

$$125\,\% = 125/100 = 5/4$$ 
We can write the obtained fraction as a ratio i.e .$$5/4 = 5:4$$


Express each of the following per cents as decimals: $$128.8\%$$

$$128.8$$%
$$=128.8\times \dfrac{1}{100}$$
$$=\dfrac{128.8}{100}$$
$$=1.288$$


Write each of the following as percent : $$ \dfrac{5}{8} $$


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A chair is bought by a trader  at $$20\% $$ discount on its marked price. The marked price is Rs $$7,200$$. If he sells it at $$16\%$$ discount on its marked price, find the profit percent made in the whole transaction.

Brought cost of chair after $$20 \%$$ discount $$=$$ $$\dfrac{7200\times80 }{100}= 5760$$
Selling cost after $$16 \%$$ discount $$=$$ $$\dfrac{7200\times84 }{100}= 6048$$ 
Profit on chair $$=$$ $$6048-5760=288  \ Rs $$
$$\%$$ of profit $$=$$ $$\dfrac{288\times100 }{5760}= 5$$ $$\% $$


A shopkeeper makes a profit of 20% on selling a transistor radio for Rs.For how much should he sell another transistor radio, whose cost price is Rs. 25 more than the first one, to make the same percentage profit ?

Case 1:
S.P of transistor=840  Rs.
Profit=20%
Then $$C.P.=\left(\dfrac{100}{120}\right)\times840=700  Rs.$$
Case 2:
C.P.of transistor =700+25=725 Rs.
Profit=20%
Then$$S.P=\left(\dfrac{120}{100}\right)\times725=870  Rs.$$ 



By selling tea for $$Rs \ 67.20$$ per kg, a profit of $$12\%$$ is made, Find quantity of tea ( in kg ) bought and sold in order to gain $$Rs \ 144.$$

Given,  Profit % by selling 1 kg of tea $$ = \dfrac {S.P - C.P.}{C.P.} \times 100 = 12 $$ %
$$ => \dfrac {67.20- C.P.}{C.P.} \times 100 = 12 $$
$$ => 67.20- C.P. = 0.12 C.P. $$
$$ => 1.12 C.P. = 67.20 $$
$$ C.P. = Rs  60 $$
$$ => Profit per  kg  = SP -CP = Rs 67.20 - Rs 60 = Rs  7.20 $$
To gain $$ Rs  144 $$, number of kg of tea bought and sold $$ = \dfrac {144}{7.20} = 20  kg $$


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.

Profit sharing ratio $$= 15000 : 18000 = 5 : 6 $$
Total profit $$= 8800$$
Nitesh gets 12.5 % of the profit = $$\displaystyle \frac{12.5}{1000}\times 8800=Rs.1100$$
Net profit $$= 8800 - 1100 = Rs. 7700$$
Nitesh share in profit = $$\displaystyle \frac{5}{5+6}\times 7700=Rs.3500$$
Total profit of Nitesh $$= 3500 + 1100 = Rs. 4600$$


A and B invested Rs 3600 and Rs 4800 respectively to open a shop. At the end of the year B's profit was Rs 1208 Find A's profit Rs ......

Profit sharing ratio = 3600 : 4800 = 3 : 4
$$\displaystyle \frac{Profit\: of\: A}{Profit\: of\: B}=\frac{3}{4}$$
$$\therefore$$ Profit of A = $$\displaystyle \frac{3}{4}$$ Profit of B
$$\Rightarrow$$ Profit of A = $$\displaystyle \frac{3}{4}\times 1208 = Rs.906$$



A vendor bought $$20$$ oranges for Rs $$56$$ and sold them at Rs $$35$$ per dozen. If his gain or loss percent is given by $$\dfrac pq\%$$, where $$p$$ and $$q$$ are co-primes, then find the value of $$p-q$$.

Let the number of oranges bought $$=$$ LCM of $$20$$ and $$12 = 60$$.                  $$\because$$ he sold in dozens i.e, in multiples of $$12$$
C.P. of $$20$$ oranges $$=$$ Rs.$$56$$  
$$\therefore$$ C.P. of $$1$$ orange $$=$$ Rs. $$\displaystyle \frac{56}{20}$$
Hence the C.P. of $$60$$ oranges $$=$$ Rs.$$\displaystyle \left ( \frac{56}{20}\times 60 \right )=$$ Rs. $$168$$
S.P. of $$12$$ oranges $$=$$ Rs. $$35$$ 
$$\therefore$$ S.P. of $$1$$ orange $$=$$ Rs. $$\displaystyle \frac{35}{12}$$
Hence, the S.P. of $$60$$ oranges $$=$$ $$\displaystyle \left ( \frac{35}{12}\times 60

\right )=Rs.175$$ 
Thus C.P. $$=$$ Rs.168 and S.P. $$=$$ Rs. $$175$$
Since (S.P.) $$>$$ (C.P.) So, the vendor has made a gain
Gain $$= (175 - 168) =$$ Rs. $$7$$  
$$\therefore$$ Gain $$\%$$ $$=$$ $$\displaystyle \left (

\frac{Gain}{C.P.}\times 100 \right )\%=\left ( \frac{7}{168}\times 100

\right )\%=\dfrac{25}{6}\%$$
We can see that, $$p=25$$ and $$q=6$$ and both are coprimes
Thus, $$p-q=25-6=19$$


Ramesh started a business by investing $$Rs 25000$$.  $$3$$ months later Mahesh joined the business by investing $$Rs 25000$$. At the end of the year Ramesh got $$Rs 1000$$ more than Mahesh out of the profit Find the total profit in $$Rs$$

Ramesh invested for $$12$$ month Mahesh invested for $$9$$ month
$$\therefore$$ Profit sharing ratio = $$12x : 9x = 12 : 9 = 4 : 3 $$
Let Capital be $$Rs.P$$ 
Profit of Ramesh = $$ \dfrac{4}{7}P$$

Profit of Mahesh = $$ \dfrac{3}{7}P$$

According to the question
$$ \Rightarrow \dfrac{4}{7}P=\dfrac{3}{7}P+1000$$

$$ \Rightarrow \dfrac{4}{7}P-\dfrac{3}{7}P=1000$$

$$\Rightarrow \dfrac{P}{7}=1000\Rightarrow P=Rs.7000$$


Rajeev & Sanjeev entered into a partnership and invested Rs 36000 and Rs 40000 respectively. After 8 months, Rajeev invested an additional capital of RsSanjeev withdraw Rs 4000 after 9 months. At the end of the year, total profit was RsFind the difference in the profits of each.

Rajeev's capital $$=36000 \times  8 + (36000 + 4000) \times  4 $$
$$=288000 + (40000 \times 4)$$
$$=288000 + 160000$$
$$= \text{ Rs. } 448000$$

Sanjeev's capital $$= 40000 \times  9 + (40000 - 4000) \times  3 $$
$$=360000 + (36000 \times 3)$$
$$=360000 + 108000$$
$$= \text{ Rs. } 468000$$

Profit sharing ratio $$=448000 : 468000 = 112 : 117$$

Rajeev's profit $$=\dfrac{112}{112+117}\times 45800=\text{ Rs. }22400$$

Sanjeev's profit $$=\dfrac{117}{112+117}\times 45800=\text{ Rs. }23400$$


Suresh & Ramesh entered into a partnership by investing Rs 14000 and Rs 18000 respectively. Suresh with drew his money after 4 months. If the total profit at the end of the year is Rs 12240 find the profit difference in Rs

Suresh invest 1400 for 4 months
Ramesh invest 18000 for 12 months
Profit sharing ratio =$$ 14000 \times  4 : 18000 \times 12 = 7 : 27$$
Suresh's profit = $$ \dfrac{7}{34}\times 12240=Rs.2520$$
Ramesh's profit = $$ \dfrac{27}{34}\times 12240=Rs.9720$$


A person buys $$120$$ shares at a nominal value of $$Rs. 40$$ each, which he sells at $$Rs. 42.50$$ each. Find his profit.

Nominal value of 1 share = Rs.40
$$\therefore $$ nominal value of 120 shares$$=120\times 40=Rs.4800$$
S.P of 1 share = Rs.42.50
$$\therefore$$ S.P of 120 share$$=120\times 42.50=Rs.5100$$
Profit$$=5100-4800=Rs.300$$


Convert the following ratios to percentages.
(a) $$3 : 4$$
(b) $$2 : 3$$

Converting a ration into percentage means making the denominator of the fraction $$=100$$.
Multiply the fraction by 100 & add the % symbol.

a)  $$3:4 = \dfrac 34 = \dfrac {3 \times 25}{4 \times 25} =  \dfrac {75}{100} = 75 \%$$

b)  $$2:3 = \dfrac 23 = \dfrac {2 \times 100}{3 \times 100} =  \dfrac {200}{3 \times 100} = \dfrac {66.66}{100} = 66.66 \%$$


A milkman sold two of his buffaloes for $$Rs. 20,000$$ each. On one he made a gain of $$5$$% and on the other a loss of $$10$$%. Find his overall gain or loss. 

Sp of buffalo1 $$=$$ Rs $$20,000$$
Gain $$= 5\%$$
So, Cost price of buffalo1 $$= \dfrac { 100 }{ 105 }\times20,000=$$ Rs. $$19047.62$$

SP of buffalo2 $$=$$ Rs $$20,000$$
Loss $$= 10\%$$
Cost price of buffalo2 $$= \dfrac { 100 }{ 90 } \times20,000 =$$ Rs $$22,222.22$$

Total Cost price $$=$$ Rs $$41269.84$$
Total selling price $$=$$ Rs $$40,000$$
Loss $$=$$ Rs $$1269.84$$


A trip of Saurashtra was organised by the school in a mini bus for 28 students and in a regular bus for 45 students. Each student contributed RsDuring the trip, the expenses were : food bill Rs 9,855, entry fees Rs 3,285, mini bus charge Rs 5,432, the regular bus charge Rs 8,730 and boarding charge Rs 6,132.  How much money (in rupees) will each student get as refund, if any?

Total money taken from student $$=500 \times (28+45)=36500$$

Total money spent $$=9855+3285+5432+8730+6132$$

Since total money left in excess after all expenses$$=Rs.\ 3066$$ and

Total number of students$$=73$$

Hence the refund each student will get

$$=\dfrac{3066}{73}=Rs.\ 42$$


Calculate the profit 
A refrigerater bought for $$Rs\ 12,000$$ and sold at $$Rs\ 13,500$$.

Cost price of refrigerator $$= Rs. 12000$$
Selling price of refrigerator $$= Rs. 13500$$
Therefore,
Profit $$=$$ Selling price $$-$$ Cost price
$$\therefore$$ Profit $$= 13500 - 12000 = Rs. 1500$$



Express each of the following as a per cent 
(i) $$\dfrac { 5 } { 8 }$$                    

$$(i)\quad \dfrac{5}{8}\times 100=\dfrac{5\times 25}{2}\%=\dfrac{125}{2}\%$$
                                                $$=62.5\%$$



If $$C.P=Rs7.5$$ and $$S.P=Rs8.5$$ then find profit $$(\%)=?$$

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

$$=\dfrac{8.5- 7.5}{7.5}\times 100$$

$$=\dfrac{100}{7.5}$$

$$= 13.33\%$$

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Express the following fractions as percents:
$$( i ) \dfrac { 1 } { 2 } \quad ( ii ) \dfrac { 17 } { 25 } (iii) \dfrac { 3 } { 8 } \quad \text { (iv) } 2 \dfrac { 7 } { 16 } (v) \dfrac { 14 } { 75 }$$

(i) $$\cfrac{1}{2}\times 100=50\%$$

(ii) $$\cfrac{17}{25}\times 100=68\%$$

(iii) $$\cfrac{3}{8}\times 100=37.5\%$$

(iv) $$2\cfrac{7}{16}\times 100=243.75\%$$

(v) $$\cfrac{14}{75}\times 100 =18.66\%$$



$$CP=$$$$Rs. 675$$ and $$SP =Rs. 630$$. Find loss

Given:
$$CP=Rs.\ 675 $$
$$SP=Rs\  630$$

$$\Rightarrow \text {Loss}=CP-SP$$
               $$=675-630$$
               $$=Rs\ 45$$


Find the gain or loss percent if
$$C.P.=Rs.550$$ and $$gain=Rs.22$$

$$CP = 550$$
$$gain = 22$$
$$gain\%  = \frac{{22}}{{550}} \times 100$$
$$ = 4\% $$


A vendor bought sweets for $$Rs. 50$$ and sold these for $$Rs. 80$$ to school children. Find his profit percentage.

Given that,
$$C.P.=Rs.\ 50$$
$$S.P.=Rs.\ 80$$

We know that, $$Profit \% = \dfrac{SP-CP}{CP}\times 100   $$

$$= \dfrac{80-50}{50}\times 100 $$

$$ \dfrac{30}{50}\times 100  $$

$$=60\%$$

Hence, the profit $$60\%$$.


Express $$52:100$$ as percentage and write an equivalent fraction.

Given$$:\ 52:100$$

Converting to percentage $$=\dfrac{52}{100}\times 100$$

                                             $$=52\%$$

Now, $$52\% = \dfrac{52}{100}$$ 

                  $$= \dfrac{13}{25}$$

Equivalent fraction is $$\dfrac{13}{25}$$


Cost price of a article is $$R s .1000$$ and selling price is $$Rs.920$$. Find the loss. 

Given cost price of book is $$CP=Rs.1000$$
Selling price of book is $$SP=Rs.920$$
Loss $$=CP-SP=1000-920=Rs.80$$


The CP of a product is $$450$$ and SP is $$500$$. Find the Profit %.

The CP of product is $$\text{Rs. } 450$$
The SP of Product is $$\text{Rs. } 500$$
The profit $$\%$$ is given as $$\cfrac{SP-CP}{CP}\times 100$$
$$=\cfrac{500-450}{450}\times 100$$
$$=\cfrac{50}{450}\times 100$$
$$=\cfrac{100}{9}$$
$$=11.11\%$$


The CP of product is $$720$$ The SP is $$1000$$ find the proft $$\%$$

The CP of product is $$720Rs.$$
The SP of Product is $$1000Rs.$$
The profit $$\%$$ is given as $$\dfrac{SP-CP}{CP}\times 100\\\dfrac{1000-720}{720}\times 100 \\\dfrac{280}{720}\times 100\\\dfrac{100\times 7}{18}=38.8\%$$


Convert$$\dfrac{7}{20}$$ to per cent.

$$\dfrac{7}{20} = \dfrac{7}{20} \times 100 \% = 35 \%$$


Write $$\dfrac { 19 }{ 100 } $$ as percentage.

$$=\cfrac { 19 }{ 100 } \times 100$$%
$$=19$$%


Express $$\dfrac { 9 }{ 100 } $$ as percentage.

$$\cfrac { 9 }{ 100 } $$
$$=\cfrac { 9 }{ 100 } \times 100=9$$%


A retailer buys a radio for RsHis overhead expenses are RsIf he sells the radio for Rs 300, determine his profit (in percent).

$$\text{Cost price of radio= Bought price+overhead expanses}$$

Hence, $$CP=Rs.\ (225+15)=Rs.\ 240$$

$$SP=Rs.\ 300$$.

Since, $$SP>CP$$, so retailer get profit.

$$Profit=SP-CP=300-240=Rs.\ 60$$

$$Profit(\%)=\dfrac{profit}{CP}\times 100=\dfrac{60}{240}\times 100=25\%$$


By selling a book for Rs 285, a bookseller gains 20%. For how much should he sell it to gain 30% (correct upto two decimal places)?

Selling price of the book, $$\mathrm{S} . \mathrm{P}$$ $$=\mathrm{Rs.}\space 285$$ 
and, $$\operatorname{Gain} \%=20 \%$$
$$\therefore$$ Cost price of the book, $$\mathrm{C} . \mathrm{P}=\left[\frac{100}{100+\mathrm{Gain} \%} \times \mathrm{S} . \mathrm{P}\right]$$
$$\Rightarrow \mathrm{C.P}=\left[\frac{100}{100+20} \times 285\right]$$
$$\Rightarrow \mathrm{C.P}=\frac{28500}{120}$$
$$\Rightarrow \mathrm{C.P}=\mathrm{Rs}. \space237.5$$
Let the bookseller sells it for  $$\mathrm{Rs.} \space x$$.
So, $$\mathrm{S} . \mathrm{P}$$ $$=\left[\frac{100+\operatorname{Gain} \%}{100} \times \mathrm{C} . \mathrm{P}\right]$$
$$\Rightarrow x=\frac{100+30}{100} \times 237.5$$
$$\Rightarrow x=\frac{130 \times 237.5}{100}$$
$$\Rightarrow x=\mathrm{Rs.} \space308.75$$
So, Bookseller must sell it for $$\mathrm{Rs.}\space 308.75$$ in order to gain $$30 \% .$$



Jitendra set up a factory by investing Rs $$2500000$$. During the first two successive years, his profits were $$5\%$$ and $$10\%$$ respectively. If each year the profit was on the previous year's capital, compute his total profit. (In Rs) 

Here, 
$$P=Rs.25,00,000$$
$$R=5\%$$
Amount at the end of the first year $$=P\left(1+\dfrac{R}{100}\right)$$

                                                  $$=2500000\left(1+\dfrac{5}{100}\right)$$

                                                  $$=2500000(1.05)$$

                                                  $$=26,25,000$$
Now, for second year

$$P=Rs.26,25,000$$
$$R=10\%$$
Amount at the end of the second year $$=P\left(1+\dfrac{R}{100}\right)$$

                                                        $$=2625000\left(1+\dfrac{10}{100}\right)$$

                                                        $$=2625000(1.10)$$

                                                        $$=28,87,500$$

Total profit $$=Rs(2,887,500-2,500,000)$$
                 $$=Rs.3,87,500$$




By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?

S.P of $$90$$ ball pens $$= \mathrm{Rs.} \space160$$ 
$$\mathrm{Loss} \%=20$$
$$\therefore$$ C.P of $$90$$ ball pens $$=\mathrm{S.P}\left(\dfrac{100}{100-\mathrm{Loss} \%}\right)$$
$$=160\left(\dfrac{100}{100-20}\right)$$
$$=\dfrac{16000}{80}$$
$$=\mathrm{Rs.}\space 200$$ 
$$\therefore$$ C.P of $$1$$ ball pen $$=\mathrm{Rs.} \space\dfrac{200}{90}= \mathrm{Rs.}\space \dfrac{20}{9}$$
Let us suppose $$x$$ ball pens are sold to earn a profit of $$20 \%$$
Then, C.P of $$x$$ ball pens $$= \mathrm{Rs.} \space\dfrac{20}{9} x$$
and S.P of $$x$$ ball pens is given as $$\mathrm{Rs.} \space96$$ 
Given $$\mathrm{Profit}\% =20$$ 
C.P of $$90$$ ball pens $$=\operatorname{S.P}\left(\frac{100}{100+\text { Profit } \%}\right)$$
$$\Rightarrow \dfrac{20}{9} x=96\left(\dfrac{100}{100+20}\right)$$
$$\Rightarrow \dfrac{20}{9} x=\dfrac{9600}{120}$$
$$\Rightarrow x=80 \times \dfrac{9}{20}$$
$$\Rightarrow x=36$$
$$\therefore 36$$ ball pens should be sold for $$\mathrm{Rs.}\space 96$$ so as to earn a profit of $$20 \% .$$


A retailer buys a cooler for Rs 1200 and overhead expenses on it are RsIf he sells the cooler for Rs 1550, determine his profit (in percent).

$$\text{Cost price of cooler= Bought price+overhead expanses}$$

Hence, $$CP=Rs.\ (1200+40)=Rs.\ 1240$$

$$SP=Rs.\ 1550$$.

Since, $$SP>CP$$, so retailer get profit.

$$Profit=SP-CP=1550-1240=Rs.\ 310$$

$$Profit(\%)=\dfrac{profit}{CP}\times 100=\dfrac{310}{1240}\times 100=25\%$$


Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%. At what gain percent she must sell the remaining hens so as to gain 20% on the whole?

Given, Toshiba bought 100 hens for Rs. 8000
and sold 20 at gain = 5 %
to gain 20 % in whole.
Cost price (CP) of 100 hens = Rs 8000
Cost price of 1 hen $$= \dfrac{8000}{100} \\ = Rs. 80$$
So, cost price of 20 hens $$= 20 \times 80 \\ = Rs. 1600$$
Gain % $$ = \dfrac{SP - CP }{CP} \times 100 \\ 5 = \dfrac{SP - 1600}{1600} \times 100 \\ SP = \dfrac{5 \times 1600}{100} + 1600 = Rs. 1680 $$
$$ \therefore $$ Gain on 20 hens = (1680 - 1600) = Rs .80
Now, cost price of 80 hens $$ = 80 \times 80 \\ = Rs. 6400 $$
Gain on 80 hens = ( SP - CP) of 80 hens
Gain on 100 hens = gain on 80 hens + gain on 20 hens 
$$ \therefore $$ Gain on 100 hens = (SP - CP) of 80 hens + 80 
Gain % on 100 hens $$= \dfrac{\textrm{Gain on 100 hens}}{\textrm{CP of hens}} \times 100 \\$$
$$ \therefore 20 = \dfrac{\textrm{(SP of 80 hens - 6400 + 80 )}}{8000} \times 100 \\$$
$$ \therefore $$ SP of 80 hens $$ = \dfrac{8000 \times 20}{100} + 6400 - 80 \\ = 1600 + 6400 - 80 = Rs. 7920$$
$$ \therefore $$ Gain of 80 hens $$ = 7920 - 6400 \\ = Rs. 1520 $$
$$ \therefore \dfrac{\textrm{Gain on 80 hens}}{\textrm{C.P. of 80 hens} } \times 100 = \textrm{gain %} = \dfrac{1520}{6400} \times 100 = 23.75 \% $$
So, the remaining hens should be sold at 23.75 % gain percent.


A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 gm for kilogram. Thus his gain percent is $$a\dfrac bc \%.$$
Find the value of $$a+b+c$$

He sells $$950 \space \mathrm{gm}$$ pulses and gets a gain of $$50\space \mathrm{gm}\space(=1000\space \mathrm{gm}-950\space \mathrm{gm})$$ 
If he sells $$100\space \mathrm{gm}$$ of pulses, he will gain $$=\left[\frac{\text { Error }}{(\text { True value })-(\text { Error })} \times 100\right] \%$$ 
$$=\left(\frac{50}{1000-50} \times 100\right) \%$$
$$=\frac{5000}{950} \%$$
$$=\frac{100}{19} \%$$
$$=5 \frac{5}{19} \%$$
$$\therefore$$ His gain percent is $$5 \frac{5}{19} \%$$

$$a+b+c=29$$


If the cost price of 18 chairs be equal to selling price of 16 chairs, find gain or loss (in percent).

Let, $$CP$$ of $$1$$ chair be $$x$$.

$$CP$$ of $$18$$ chairs is $$18x=SP$$ of $$16$$ chairs.

$$CP$$ of $$16$$ chairs $$=16x$$

Since, $$SP>CP$$

$$Profit =SP-CP$$

$$=18x-16x=2x$$

$$Profit(\%)=\dfrac{profit}{CP}\times100$$

$$=\dfrac{2x}{16x}×100$$

$$=\dfrac{100}{8}=12.5 \%$$


If the selling price of 10 pens is equal to cost price of 14 pens, find the gain (in percent).

Let the $$CP$$ of $$1$$ pen be $$Rs\ x$$
Then,
$$CP$$ of $$14$$ pens will be $$14×x=14x$$
And
$$CP$$ of $$14$$ pens=$$SP$$ of $$10$$ pens
Hence,
$$SP$$ of $$10$$ pens $$= 14x$$
Then,,
$$SP$$ of $$1$$ pen$$=14x÷10=1.4x$$

$$Gain=SP-CP. = 1.4x - x= Rs 0.4x$$
$$Gain(\%)=\dfrac{gain}{CP}×100$$
$$=\dfrac{0.4x}{x}×100 =40\%$$


Express the following ratio as percentage: $$1:5$$

Given : 
1:5
Converting to %....
$$\frac{1}{5}\times{\frac{100}{100}}$$
$$\frac{20}{100}$$
$$=20\%$$


Express the following ratios as percentage: $$4:5$$

Given : 
4:5
Converting to %....
$$\frac{4}{5}\times{\frac{100}{100}}$$
$$\frac{80}{100}$$
$$=80\%$$


Express the following percents as fractions in the simplest forms: 45%

$$45\%=\dfrac{45}{100}$$=$$\dfrac{9}{20}$$


Given the following values, find the unknown values:
C.P = Rs 980, S.P. = Rs 940, Profit/Loss = ?

As $$S.P < C.P$$
$$Loss=C.P-S.P$$
$$Loss=980-940$$
$$Loss=Rs\ 40$$


Mr Virmani purchased a house for Rs 365000 and spent Rs 135000 on its repairs. If he sold it for Rs 550000, find his gain percent.

Amount Mr. Virmani paid to purchase the house $$= Rs. 365000$$
Amount he spent on repair $$= Rs. 135000$$
Total amount he spent on the house $$(CP) = Rs. (365000 + 135000) = Rs. 500000$$
SP of the house $$= Rs. 550000$$
$$Gain = SP - CP = Rs. (550000 - 500000) = Rs. 50000$$

$$Gain \% = (Gain/CP) ×  100 = (50000/500000) × 100 = 5000000/500000 = 10\%$$


Calculate the profit or loss and profit or loss per cent in each of the following cases: 
C.P = Rs 332, S.P. = Rs 350

$$Profit=S.P-C.P$$
Let $$profit\ be\ x$$
$$x=350-332$$
$$x=18$$
Profit $$= Rs. 18$$
Profit $$\% = \dfrac{18}{332}\times 100 \%$$
Profit $$\% = 5.42\%$$

$$Profit = Rs. 18$$
$$Profit\,  \% = 5.42\%$$


Fill in the blanks in each of the following:
C.P. = Rs 3355, S.P = Rs 7355,  ..... = Rs .....

$$Profit=S.P-C.P$$
Let $$profit\ be\ x$$
$$x=7355-3355$$
$$x=4000$$


Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for RsFind her gain percent.

The cost price of the wristwatch that Shikha purchased, $$CP = Rs. 840$$
The price at which she sold it, $$SP = Rs. 910$$
$$Gain = SP - CP$$
         $$= (910 - 840) = Rs. 70$$

$$Gain \% = (Gain/CP) ×  100 = (70/840) × 100 = 7000/840 = \dfrac{25}{3}\%$$


Express $$12.5\%$$ in decimals.

$$12.5$$%
$$=12.5\times \dfrac{1}{100}$$
$$=\dfrac{12.5}{100}$$
$$=0.125$$


Find the gain or loss per cent, when:
C.P. = Rs 4000 and gain = Rs 40.

Profit $$= Rs. 40$$
C.P$$=Rs. 4000$$
Profit $$\% = \dfrac{40}{4000}\times 100 \%$$
Profit $$\% = 1\%$$

Gain $$= 1\%$$


Fill in the blanks in each of the following:
C.P. = Rs 1265, S.P = Rs 1253, Loss  Rs .....

As $$C.P>S.P$$
$$Loss=C.P-S.P$$
$$Loss=1265-1253$$
$$Loss=Rs\ 12$$


Find the profit or loss per cent, when:
S.P. = Rs.1820 and profit = Rs.420.

Profit$$=S.P-C.P$$
Let $$C.P\ be\ x$$
$$420=1820-x$$
$$x=1400$$
C.P$$=Rs. 1400$$
Profit $$= Rs. 420$$
Profit $$\% = \dfrac{420}{1400}\times 100 $$
Profit $$\% = 30\%$$

Gain $$= 30\%$$


Express each of the following as decimal:

i. $$6\,\%$$ 
ii. $$72\,\%$$ 
iii. $$125\,\%$$ 

We know the number has to be divided by 100 we get,

i. $$6\,\% = 6/100 = 3/50 = 0.06$$ 
ii. $$72\,\% = 72/100 = 18/25 = 0.72$$ 
iii. $$125\,\% = 125/100 = 5/4 = 1.25$$


Find the gain or loss percent when $$CP=₹620$$ and $$SP=₹713$$.

We know that $$SP$$ is more than $$CP$$ so it's a gain.

As the formula states, $$Gain = SP - CP$$

$$713-620=93$$

$$Gain\%=(Gain\times100)/CP$$
     
               $$=(93\times100)/620$$

               $$=15\%$$


Express each of the following as a percentage:

i. $$9/25$$
ii.$$ 3/125$$ 
iii. $$12/5$$ 

We know the number has to be multiplied by 100 we get,

i.  $$ 9/25 = ((9/25) \times 100) \,\% = ( 9 \times 4) \,\% = 36\,\% $$
ii. $$3/125 = ((3/125) \times 100) \,\% = 2.4\,\% $$
iii.$$12/5 = ((12/5) \times 100)\,\% = (12 \times 20)\,\% = 240\,\% $$


Convert each of the following ratios into a percentage:
$$37:100$$

First convert the given ratio into fraction, and then multiply the fraction by $$100$$ and put the percent sign $$\%$$
$$=(37/100)$$
$$=(37/100)\times 100$$
$$=37\%$$


Express each of the following as a ratio:
$$36\%$$

Percentage can be expressed as a ratio by dividing it by $$100$$
We have
$$\Rightarrow \dfrac{36}{100}$$
$$\Rightarrow 36:100$$


Convert each of the following ratios into a percentage:
$$16:25$$

First, convert the given ratio into a fraction, and then multiply the fraction by $$100$$ and put the percent sign $$\%$$
$$16:25=\dfrac{16}{25}$$

             $$=\dfrac{16}{25}\times 100\%$$

             $$=16\times 4\%$$

             $$=64\%$$


Convert each of the following ratios into a percentage:
$$3:5$$

First convert the given ratio into fraction, and then multiply the fraction by $$100$$ and put the percent sign $$\%$$
$$=(3/5)$$
$$=(3/5)\times 100$$
$$=(3\times 20)$$
$$=60\%$$


Convert each of the following into a fraction:
$$120\%$$

To convert a percentage into a fraction, we divide it by $$100$$ and remove the sign $$\%$$
As per the given condition,
$$120\%=\dfrac{120}{100}$$
         $$=\dfrac{6}{5}$$


Express each of the following as a ratio:
$$43\%$$

Percentage can be expressed as a ratio with its second term is $$100$$ and first term is equal to the given percentage.
We have,
$$=(43/100)$$
$$=43:100$$


Convert the each of the following into decimal form:
$$127\%$$

First convert the given percentage into fraction and then put the fraction into decimal form.
$$=(127/100)$$
$$=1.27$$


Convert the following ratio into a percentage:
$$5:4$$

Ratio can be converted into percentage by first converting the given ratio into fraction, and then multiplying the fraction by $$100$$ and put the percent sign $$\%$$:
$$5:4=\dfrac{5}{4}$$
     $$=\dfrac{5}{4}\times 100\%$$
     $$=(5\times 25)\%$$
     $$=125\%$$


Fill in the blanks to make the statement true.
$$2 : 3 = ......\%$$

$$\Rightarrow 2 : 3 = \dfrac{2}{3}$$

$$= 0.66 = \dfrac{66}{100} = 66\%$$

$$2 : 3 = 66\%$$


Fill in the blanks to make the statement true:
To convert a fraction into a per cent, we ............. it by $$100.$$

To convert a fraction into a per cent, we multiply it by $$100.$$


Fill in the blanks to make the statement true.
$$\dfrac{8}{5} = .......\%$$

$$ \dfrac{8}{5} = 1.6$$

$$\Rightarrow \dfrac{16}{10} \times \dfrac{10}{10}$$

$$\Rightarrow \dfrac{160}{100}$$

$$\Rightarrow 160\%$$


In a furniture shop, $$24$$ tables were bought at the rate of $$Rs.450$$ per table. The shopkeeper sold $$16$$ of them at the rate of $$Rs.600$$ per table and the remaining at the rate of $$400$$ per table. Find her gain or loss percent.

Cost price of 1 table $$= Rs.450$$
Hence, cost price of $$24$$ tables $$= 24 \times 450 = Rs.10800$$
Selling price of $$16$$ tables $$= 16 \times 600 = Rs.9600$$
Selling price remaining tables $$(8)$$
$$= 8 \times 400 = Rs.3200$$
Selling price of $$24$$ tables $$= 9600 + 3200 = 12800$$
Here, $$S.P. > C.P.$$
Therefore, gain of $$= 12800 - 10800 = Rs.2000$$
$$Gain\% = \dfrac{2000}{10800} \times 100 = 18.5\%$$


Convert the following percentage into ratios in sirup rest form:
$$33 \dfrac{1}{3}\%$$

$$33 \dfrac{1}{3}\% = \dfrac{100}{3 \times 100} = \dfrac{1}{3} = 1 : 3$$


Convert the following fractions into percents.
$$\dfrac{1}{8}$$

$$\dfrac{1}{8} = \dfrac{1 \times 100}{8} = \dfrac{25}{2}\% = 12.5\%$$


Express the following ratios as percentages:
$$1 : 1$$

$$1 : 1 = \dfrac{1}{1} \times 100 = 100\%$$


Convert the following percentage into ratios in sirup rest form:
$$37.5\%$$

$$37.5\% = 37\dfrac{1}{2}\% = \dfrac{75}{2}\% = \dfrac{75}{2 \times 100}  = \dfrac{3}{8} = 3 : 8$$


Convert the following fractions into percents.
$$\dfrac{9}{16}$$

$$\dfrac{9}{16} = \dfrac{9 \times 100}{16} = 56.25\%$$


Convert the following percentage into ratios in simplest form:
$$1 \dfrac{3}{4}\%$$

$$1 \dfrac{3}{4}\% = \dfrac{7}{4}\% = \dfrac{7}{4 \times 100} = \dfrac{7}{400} = 7 : 400$$


Convert the following percentage into ratios in simplest form:
$$14\%$$

$$14\% = \dfrac{14}{100} = \dfrac{7}{50} = 7 : 50$$


Convert the following fractions into percents.
$$\dfrac{3}{7}$$

$$\dfrac{3}{7} = \dfrac{3 \times 100}{7} = 42.85\%$$


Rohan bought a calculator for $$Rs.760$$ and sold it for $$Rs.874.$$ Find his profit and profit percentage.

C.P. of calculate $$= Rs.760$$
and S.P. $$= Rs.874$$
Gain = S.P. - C.P. $$= Rs.874 - Rs.760 = Rs.114$$
$$Gain\% = \dfrac{Gain \times 100}{C.P.} = \dfrac{114 \times  100}{760} = 15\%$$


Express the following ratios as percentages:
$$9 : 16$$

$$9 : 16 = \dfrac{9}{16} \times 100 $$
           
           $$= \dfrac{225}{4} = 56\dfrac{1}{4}\%$$


Express the following fractions as decimals. Then express the decimals percentages:
(i) 3/4

 $$3/4 = 0.75$$
It can be written as
$$3/4 = 3/4 \times 100%$$
By further Calculation
=$$3 \times 25%$$
=$$ 75$$%


Express the following ratio as percentages:
(i) 17 : 20

(i) $$17 : 20$$
It can be written as 
$$17 : 20 = 17/20$$
By further calculation
= $$ 17/20 \times 100%$$
So we get
= $$ 17 \times 5%$$
= $$85$$%


Express the following fractions as percentages:
(i) 9/20

 $$9/20$$
It can be written as
= $$9/20 \times 100%$$
= $$45$$%


What percent of 12 kg is 725 gm ?

We know that 
$$1 \text{ kg} = 1000 \text{ gm}$$

So we get 
$$ 12 \text{ kg} = 12 \times 1000 = 12000 \text{ gm} $$

The formula for percentage is
$$\text{Percentage} = \dfrac{a}{b} \times 100 \%$$

$$ = \dfrac{725 }{ 12000} \times 100 \% $$

$$= \dfrac{725}{120} \%$$

$$= \dfrac{145}{24}$$ % 

$$=6\dfrac{ 1}{24} \%$$

$$=6.04 \%$$

Therefore, $$6.04 \%$$ of $$12 \text{ kg}$$ is $$725 \text{ gm}$$.


Express :
3/20 as percent 

$$\dfrac {3}{20}$$ as percent 

$$= \dfrac {3}{20} \times 100 $$

$$= 15$$%


Convert the following ratio into percentage.
$$\dfrac{144}{1200}$$

$$\dfrac{144}{1200}=\dfrac{144}{1200}*100$$%

$$=\dfrac{144}{12}$$%

$$=12$$%


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

$$\dfrac{7}{16}=\dfrac{7}{16}*100$$%

= $$\dfrac{700}{16}$$%

= $$43.75$$%


Convert the following ratio into percentage.
$$15 : 25$$

$$15:25=\dfrac{15}{25}=\dfrac{15}{25}*100$$%
=$$15*4$$%= $$60$$%.


Convert the following ratio into percentage.
$$47 : 50$$

$$\Rightarrow 47:50=\dfrac{47}{50}$$
to convert ratio into percentage we need to multiply the fraction by $$100$$
$$=\dfrac{47}{50}\times 100$$%
$$=47\times 2$$% = $$94$$%.


Express the following percentage as ratios in the reduced form.
$$6.25$$%

$$6.25$$%

$$\dfrac{6.25}{100}=\dfrac{625}{10000}=\dfrac{625\div625}{10000\div625}=\dfrac{1}{16}=1:16$$

(HCF of $$625$$ and $$10000=625$$)


Convert the following ratio into percentage.
$$\frac{22}{30}$$

$$\dfrac{22}{30}=\dfrac{22}{30}*100$$%

$$=\dfrac{2200}{30}$$%

$$=73.33$$%


Convert the following ratio into percentage.
`$$\dfrac{546}{600}$$`

$$\dfrac{546}{600}=\dfrac{546}{600}\times 100\%$$

         $$=\dfrac{546}{6}\%$$

         $$=91\%$$.


Convert the following ratio into percentage.
`$$\dfrac  7 {10}$$`

$$\dfrac{7}{10}=\dfrac{7}{10}*100$$%

= $$7*10$$% = $$70$$%


Convert the following ratio into percentage.
$$37 : 500$$

$$37:500=\dfrac{37}{500}*100$$%

$$=\dfrac{37}{5}$$%

$$=7.4$$%.


Convert the following ratio into percentage.
$$\dfrac{5}{8}$$

$$\dfrac{5}{8}=\dfrac{5}{8}\times100\%$$

$$=\dfrac{500}{8}\%$$

$$=62.5\%$$


Find the profit or loss $$\%$$ where:-
(i) $$CP=Rs 400$$     $$SP=Rs 300$$

Here, SP<CP 
So, We can see that we are dealing with loss 

Therefore, loss $$\%=\dfrac{loss}{CP}*100=\dfrac{CP-SP}{CP}*100=\dfrac{400-300}{400}*100=25\%$$ 


Aman started a factory with an initial investment of RsIn the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.


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Class 7 Maths Extra Questions