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CBSE Questions for Class 8 Maths Linear Equations In One Variable Quiz 2 - MCQExams.com
CBSE
Class 8 Maths
Linear Equations In One Variable
Quiz 2
A number is doubled and 9 is added If the result is trebled it becomes 75 What is that number?
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0%
3.5
0%
6
0%
8
0%
7
Explanation
Let the number be x
According to the question
3 ( 2x + 9) = 75 $$\displaystyle \Rightarrow $$ 6x + 27 = 75
$$\displaystyle \Rightarrow $$ 6x = 75 - 27 = 48 $$\displaystyle \Rightarrow $$
x = 8
4 is added to a number and the sum is multiplied byIf 20 is subtracted from the product and the difference is divided by 8 the result is equal toFind the number.
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0%
$$16$$
0%
$$12$$
0%
$$8$$
0%
$$20$$
Explanation
Let, the number be $$x$$
A.T.Q,
$$ \dfrac{5(4+x)-20}{8}=10$$
$$\implies 5(4+x)-20=10 \times 8$$
$$\implies 20+5x=80+20$$
$$\implies 5x=100-20$$
$$\implies x=\dfrac{80}{5}=16$$
$$\therefore$$ the number is $$16$$
One third of a pole is painted yellow one-fifth is painted white and the remaining 7 meters is painted black the length of the pole is
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0%
15 m
0%
30 m
0%
$$\displaystyle 10\frac{7}{15}$$ m
0%
$$\displaystyle 7\frac{1}{15}$$ m
Explanation
Let the total length of the pole be $$x$$
$$\displaystyle \frac{x}{3}+\frac{x}{5}+7=x$$
$$\displaystyle \Rightarrow \frac{5x+3x+105}{15}=x$$
$$\displaystyle \Rightarrow 8x+105 = 15x\Rightarrow 7x=105$$
$$\displaystyle \Rightarrow x=\frac{105}{7}=15$$
The sum of three consecutive multiples of 3 is 72 What is the largest number?
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0%
21
0%
24
0%
27
0%
36
Explanation
Let the three consecutive multiples of 3 be 3x, 3(x + 1) and 3 ( x + 2), i.e. 3x + 3 and 3x + 6
Given, 3x +3x + 3 + 3x +6 = 72
$$\displaystyle \Rightarrow $$ 9x + 9 = 72
$$\displaystyle \Rightarrow $$
9x=63 $$\displaystyle \Rightarrow $$ x =7
$$\displaystyle \therefore $$ Largest multiple of 3 = 3 (x + 2) =3 (7 + 2)
=3 x 9 = 27
Ram weights $$25$$ kg more than Shyam. Their combined weight is $$325$$ kg. How much does Shyam weight?
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$$150$$ kg
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$$175$$ kg
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$$200$$ kg
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$$125$$ kg
Explanation
Let Shyam's weight be $$x$$ kg.
Then, Ram's weight $$=(x+25)$$ kg
Given, the sum of their weights is $$325$$ kg. Then, we have
$$x+(x+25)=325$$
$$\Rightarrow 2x+25=325$$
$$\Rightarrow 2x=325-25=300$$
$$\Rightarrow \displaystyle x=\frac{300}{2}=150$$
$$\therefore $$ Shyam's weight $$=150$$ kg.
Ramu's father is thrice as old as Ramu. If father's age is 45 years then
Ramu's age is
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$$45 $$years
0%
$$30$$ years
0%
$$15$$ years
0%
$$10$$ years
Explanation
Let, Ramu's age be $$x$$ years
$$\therefore$$ Ramu's father's age will be $$3x$$ years
Father's age is $$45$$
$$\therefore 3x=45$$
$$\implies x=\dfrac{45}{3}=15$$
$$\therefore$$ Ramu's age is $$ 15$$ years
Shuba got three fourth of what Alka had, Alka gave half of what remained with her to Mohini If Mohini got Rs 625 how much did Alka have in the beginning?
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Rs 3750
0%
Rs 7000
0%
Rs 5000
0%
Rs 5625
Explanation
Let Alka have Rs $$x$$ in the beginning
Amount that Shubha got $$\displaystyle =Rs\frac{3x}{4}$$
Amount remaining with Alka $$\displaystyle =x-\frac{3x}{4}=Rs\frac{x}{4}$$
Amount that mohini got = $$\displaystyle \frac{1}{2}\times\frac{x}{4}=Rs\frac{x}{8}$$
Given $$\displaystyle \frac{x}{8}=625\Rightarrow x=625\times8=Rs\, 5000$$
In an examination, a student attempted $$15$$ questions correctly and secured $$40$$ marks. If there were two types of questions ($$2$$ marks and $$4$$ marks questions) how many questions of $$2$$ marks did he attempt correctly?
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0%
$$5$$
0%
$$10$$
0%
$$6$$
0%
$$7$$
Explanation
Let the number of $$2$$ marks question attempted correctly be $$x$$
Then the number of $$4$$ marks questions attempted correctly $$= ( 15 - x)$$
Total marks obtained= $$40$$
So,
$$x \times 2 + (15 - x ) \times 4 = 40$$
$$\displaystyle \Rightarrow 2x + 60 - 4x = 40$$
$$\Rightarrow -2x=-20$$
Hence, $$x=10$$.
Ramu's father is thrice as old as Ramu. If father's age is $$45$$ years, then Ramu's age is
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0%
$$45$$ yrs
0%
$$30$$ yrs
0%
$$15$$ yrs
0%
$$10$$ yrs
Explanation
Let Ramu's father's age be $$3x$$ and Ramu's age be $$x$$.
Father's age is $$45$$ years.
Then, $$3x= 45$$
$$\Rightarrow x\, =\, \displaystyle \frac {45}{3}\, =\, 15$$
$$\therefore$$ Ramu's age $$= 15$$ yrs.
A number is multiplied by $$6$$ and $$12$$ is added to the product. The result is $$84$$. Then the number is:
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0%
$$-12$$
0%
$$72$$
0%
$$+12$$
0%
$$-72$$
Explanation
Let the number be $$x$$
Then, $$x \times 6 + 12 = 84$$
$$\Rightarrow 6x = 84 -12 = 72$$
$$\Rightarrow x\, =\, \displaystyle \frac {72}{6}\, =\, 12$$
Hence required number is $$x=12$$
Twenty years ago, my age was $$\left (\displaystyle \frac{1}{3}\right)$$rd of
what it is now. What is my present age?
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0%
$$66$$ years
0%
$$30$$ years
0%
$$33$$ years
0%
$$36$$ years
Explanation
Let the present age be $$x$$ years
$$20$$ years ago, age will be $$x-20$$
As per the given condition, we have
$$x\, -\, 20\, =\, \displaystyle \frac{x}{3}$$
$$x-\dfrac {x}{3}=20$$
$$\displaystyle \frac{2x}{3}\, =\, 20$$
$$x = 30$$ years
Therefore, present age is $$30$$ years.
The number of variables in a simple linear equation is
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0%
Two
0%
One
0%
0
0%
None
Explanation
A linear equation can comprise of many variables. The most simple linear equation is in $$one$$ variable ,i.e, $$ax+b=0$$.
In $$\displaystyle \frac {a}{8}\, +\, \displaystyle \frac {a}{4}\, =\, 6$$, the value of $$a$$ is:
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0%
$$122$$
0%
$$-16$$
0%
$$16$$
0%
$$0$$
Explanation
$$\displaystyle \frac {a+2a}{8}\, =\, 6$$
$$\Rightarrow \displaystyle \frac {3a}{8}\, =\, 6$$
$$\Rightarrow 3a= 48 \Rightarrow a = 16$$
Hence the solution is $$a=16$$
The length of a rectangle is $$12$$ m and its area is $$72 m^2$$. Then the breadth equals to
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0%
$$72$$ m
0%
$$60$$ m
0%
$$6$$ m
0%
$$9$$ m
Explanation
Let $$l,b$$ and $$A$$ are length, breadth and area of the rectangle respectively.
Then given , $$l= 12$$ m, $$A = 72$$ sq.m
Now we know, area of rectangle $$=lb$$
$$\Rightarrow 12b=72$$
$$\Rightarrow b = \cfrac {72}{12}\, =\, 6\,$$ m
Hence, breadth of the given rectangle is $$6$$ m.
A person was asked to state his age in years. His reply was, take my age three years hence multiply it by $$3$$ and then subtract three times my age three years ago and you will know how old I am. What was the age of the person?
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0%
$$24$$ years
0%
$$20$$ years
0%
$$32 $$ years
0%
$$18$$ years
Explanation
Let the present age of the person be $$x$$ years
His age after $$3$$ years hence $$= (x + 3)$$ years
His age $$3$$ years ago $$= (x - 3)$$ years
Then according to given condition, his present age will be $$ (x+3) 3 - 3(x - 3)$$
$$= (3x + 9 - 3x + 9)=18$$ years.
A farmer divided his herd of x cows among his 4 sons so that one son gets one half of the herd, the second gets one-fourth, the third son gets one-fifth and the fourth gets 7 crows . Then x is
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0%
100
0%
140
0%
0
0%
1
Explanation
Given that:
No. of cows $$=x$$
According to the question,
$$\dfrac{x}{2}+\dfrac{x}{4}+\dfrac{x}{5}+7=x$$
$$\dfrac{10x+5x+4x}{20}+7=x$$
$$19x+140=20x$$
$$x=140.$$
Hence, no. of cows are $$140.$$
If the sum of $$\displaystyle\frac{1}{3}$$ and $$\displaystyle\frac{1}{4}$$ is x times the difference of $$\displaystyle\frac{1}{3}$$ and $$\displaystyle\frac{1}{4}$$, then the value of x is equal to
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0%
4
0%
5
0%
6
0%
7
Explanation
Sum of $$\frac { 1 }{ 3 } $$ and $$\frac { 1 }{ 4 } $$ is x times the difference of
$$\frac { 1 }{ 3 } $$ and $$\frac { 1 }{ 4 } $$
As per problem,
$$\Rightarrow \left( \frac { 1 }{ 3 } +\frac { 1 }{ 4 } \right) =\left( \frac { 1 }{ 3 } -\frac { 1 }{ 4 } \right)x $$
$$\Rightarrow \left( \frac { 4+3 }{ 12 } \right) =\left( \frac { 4-3 }{ 12 } \right) x$$
$$\Rightarrow \frac { 7 }{ 12 } =\frac { 1 }{ 12 } x$$
$$x=7$$
Anita had to do a multiplication. Instead of taking 35 as one of the multipliers she tookAs a result the product went up byWhat is the new product?
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0%
1050
0%
540
0%
1440
0%
1590
Explanation
Let the number that Anita wanted to multiply be 'X'.
She wanted to find the value of 35X.
Instead, she found the value of 53X.
The difference between the value that she got (53X) and what she was expected to get (35X) is 540.
Then $$53x-35x=540$$
$$18 x=540$$
$$x=30$$
$$\therefore $$ correct product is $$53\times 30=1590$$
A man has 480 rupees in the denominations of one-rupee, five rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
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0%
90
0%
75
0%
45
0%
60
Explanation
Let there be x notes of each kind
$$\implies1.x+5.x+10.x=480$$
$$\therefore x=30$$
Total number of notes $$=x+x+x=3x=90$$
The sum of a number and its half is $$84$$. Number will be-
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0%
$$65$$
0%
$$56$$
0%
$$66$$
0%
None of these
Explanation
Let the number be $$x$$
According to the question, the number$$+\cfrac{1}{2}$$ of the number $$=84$$
$$\Rightarrow$$ $$x+\cfrac{x}{2}=84$$
$$\Rightarrow$$ $$\cfrac{2x+x}{2}=84$$
$$\Rightarrow$$ $$3x=84\times 2$$
$$\Rightarrow$$ $$x=\cfrac{84\times 2}{3}$$
$$\Rightarrow$$ $$x=56$$
Hence the number is $$56$$
The sum of two consecutive natural numbers is $$23$$. Numbers will be-
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0%
$$11$$ and $$12$$
0%
$$11$$ and $$14$$
0%
$$11$$ and $$16$$
0%
$$11$$ and $$18$$
Explanation
Let the two consecutive natural numbers be $$x$$ and $$x+1$$
Now, according to the problem
$$x+(x+1)=23$$
$$\Rightarrow$$ $$2x+1=23$$
$$\Rightarrow$$ $$2x=23-1$$
$$\Rightarrow$$ $$2x=22$$
$$\Rightarrow$$ $$x=\cfrac{22}{2}=11$$
The one number is $$11$$
The next number is $$x+1=11+1=12$$
Hence the numbers are $$11$$ and $$12$$
If $$\displaystyle \frac{2}{3}$$ of a number is $$20$$ less than the
original number, then the number is
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0%
$$60$$
0%
$$40$$
0%
$$80$$
0%
$$120$$
Explanation
Let the number be $$x$$.
It is given that $$\dfrac {2}{3}$$ of a number, i.e. $$\dfrac {2}{3}x$$,
$$20$$
less than the original number, i.e. $$x-20$$.
The expression can be written as,
$$\displaystyle \frac{2}{3} x = x - 20$$
$$\therefore x = 60$$
Therefore, the number is $$60$$.
Solve : $$10(2+x) = 5(x-6)$$
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0%
$$x = 3$$
0%
$$x= -8$$
0%
$$x = -10$$
0%
$$x = 2$$
Explanation
Given, $$10(2+x) = 5(x-6)$$
or, $$20 + 10x = 5x - 30$$
Transposing 5x to LHS, we get
$$20 + 10x - 5x = -30$$
Transposing 20 to RHS, we get
$$5x = -30 -20$$
or $$5x = -50$$
Dividing both sides by 5, we get
$$\displaystyle \frac{5x}{5} = \frac{-50}{5}$$ or $$x = -10$$
Two cats Billy and Kitty together catch $$60$$ mice. If Billy catches three mice for every two caught by Kitty, then the number of mice caught by Kitty is
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0%
$$24$$
0%
$$30$$
0%
$$36$$
0%
$$40$$
Explanation
Ratio of number of mice caught by Billy and Kitty $$=3 : 2$$.
Let, the number of mice be $$3x$$ and $$2x$$
Therefore,
$$3x+2x=60$$
$$\Rightarrow 5x=60$$
$$\Rightarrow x=\dfrac {60}{5}$$
$$\Rightarrow x=12$$
Hence, number of mice caught by Kitty $$=2x$$
$$=2\times 12$$
$$=24$$
A bag contains Rs. 90 in coins. If coins of 50 paise, 25 paise and 10 paise are in te ratio 2 : 3 : 5, then the number of 25 paise coins in the bag are
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0%
120
0%
130
0%
135
0%
140
Explanation
Let the number of 50 paise ,25 paise,10paise coins be 2x,3x and 5x.
Then the sum of their values$$=(\dfrac{50\times 2x}{100}+\dfrac{25\times 3x}{100}+\dfrac{10\times 5x}{100})$$
$$\Rightarrow x+\dfrac{3x}{4}+\dfrac{x}{2}=\dfrac{9x}{4}$$
$$\therefore \dfrac{9x}{4}=90$$
$$\Rightarrow x=\dfrac{90\times 4}{9}=40$$
Hence the number of 25 paise coins=$$3x=3\times 40=120$$
If $$12 x = 4(x+3)$$, then $$x$$ equals:
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0%
$$1.5$$
0%
$$\cfrac{3}{8}$$
0%
$$5$$
0%
$$\cfrac{12}{11}$$
Explanation
Given, $$12 x = 4(x+3)$$.
$$\Rightarrow 12x=4x+12$$ ...[By Distribution Law].
Transposing $$x$$ terms to one side, we get,
$$\Rightarrow 12x-4x=12$$
$$\Rightarrow 8x=12$$
$$\Rightarrow x=\cfrac{12}{8}=\cfrac{3}{2}=1.5$$.
Hence, option $$A$$ is correct.
The difference between a number and one-fifth of it is $$100$$. What is the number?
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0%
$$125$$
0%
$$200$$
0%
$$225$$
0%
$$300$$
Explanation
Let the number is $$x$$
Then one fifth of $$x=$$ $$\dfrac{x}{5}$$
Given in question the difference of number and one fifth of number is $$100$$.
$$\therefore x-\dfrac{x}{5}=100$$
$$\Rightarrow 5x-x=500$$
$$\Rightarrow 4x=500$$
$$\Rightarrow x=125$$
If four times a number is 60 then the number is
Report Question
0%
1
0%
15
0%
60
0%
-15
Explanation
Let, the no. be $$x$$.
Acc. to question,
$$4x = 60 $$
$$x =$$ $$\displaystyle{\frac{60}{4}}=15$$
Half of a number is added to $$18$$ then the sum is $$46$$. The number is
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0%
$$92$$
0%
$$56$$
0%
$$65$$
0%
$$0$$
Explanation
Let the number be $$x$$
According to the question,
$$\Rightarrow \displaystyle \frac{x}{2}\, +\, 18\, =\, 46$$
$$\Rightarrow \displaystyle \frac{x}{2}\, =\, 46\, -\, 18\, =\, 28$$
$$\Rightarrow x =28 \times 2\, $$
$$=\, 56$$
Find the value of $$t$$, if $$8+2t=18t-7$$.
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0%
$$\dfrac{16}{15}$$
0%
$$\dfrac{-16}{15}$$
0%
$$\dfrac{-15}{16}$$
0%
$$\dfrac{15}{16}$$
Explanation
Given, $$\displaystyle 8+2t=18t-7$$.
Transposing $$t$$ terms to one side, we get,
$$\Longrightarrow\displaystyle 8+7=18t-2t$$
$$\Longrightarrow \displaystyle 16t=15$$
$$\Longrightarrow\displaystyle t=\dfrac{15}{16}$$.
Hence, option $$D$$ is correct.
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