Linear Equations in One Variable Test

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Linear Equations in One Variable Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Out of three numbers, the first is twice the second and the second is thrice the third. If the average of the three numbers is $$10,$$ find the largest number?

A
$$18$$

B
$$14$$

C
$$22$$

D
$$24$$

Solution

Let the third number be $$x$$.
Then, second number $$= 3x$$ and first number $$= 6x$$
Given, $$\displaystyle \frac{x + 3x + 6x}{3} = 10 \Rightarrow 10x = 30 \Rightarrow x = 3$$
$$\therefore$$ Largest number $$= 6x = 6 \times 3 = 18$$
Question 2
1 / -0

In a zoo there are rabbits and pigeons. If their heads are counted these are 90 while their legs are 224 The number of pigeons in the zoo are

A
70

B
68

C
72

D
22

Solution

Let the number of rabbits be $$x$$
No of heads $$\displaystyle = 90\Rightarrow $$ No of pigeons $$= (90 - x)$$
Since a pigeon has $$2$$ legs and a rabbit has 4 legs
$$x \times 4 + (90 - x) \times 2 = 224$$
$$\displaystyle \Rightarrow $$ $$4x + 180 -2x = 224$$ $$\displaystyle \Rightarrow $$ $$2x = 224 - 180 = 44$$
$$\displaystyle \Rightarrow x = 22$$
$$\displaystyle \therefore $$ No of pigeons $$= 90 - 22 = 68$$
Question 3
1 / -0

The sum of the digits of a three-digit number is $$16$$. If the ten's digit of the number is $$3$$ times the unit's digit and the unit's digit is one-fourth of the hundredth digit then what is the number?

A
$$446$$

B
$$561$$

C
$$682$$

D
$$862$$

Solution

Let the hundredth's digit of the number be $$x$$

Then unit's digit $$= \dfrac x4$$

and ten's digit $$\displaystyle=\frac{3x}{4}$$

Given,
The sum of the digits is $$16$$

$$\Rightarrow \displaystyle x +\frac{x}{4}+\frac{3x}{4}=16$$

$$\Rightarrow \dfrac{4x+x+3x}{4}=16$$

$$\displaystyle \Rightarrow 2x = 16$$

$$\Rightarrow x=8$$

ten's digit $$=\dfrac{3x}{4} = \dfrac{3 \times 8}{4} = 6$$

unit's digit $$\displaystyle =\dfrac{x}{4}=\dfrac{8}{4}=2$$

$$\displaystyle \therefore $$ Required number $$= 100 \times 8 + 10 \times 6 + 2$$

$$= 800 + 60 + 2= 862$$

The required number is $$862$$
Question 4
1 / -0

The ratio of a two digit number to the sum of its digits is $$7:1.$$ If the digit in the ten's place is $$1$$ more than the digit in the one's place, then the number is

A
$$65$$

B
$$43$$

C
$$32$$

D
$$21$$

Solution

Let the digit at the unit's place in a $$2$$ digit number be $$x$$.
Then, the digit at the ten's place $$= x + 1$$.
$$\therefore$$ The number $$= 10(x+1) + x = 11x +10$$
Sum of digits $$= x+ 1 + x = 2x + 1$$
Given, $$ \displaystyle \frac {11x+10}{2x+1} = \frac {7}{1}$$
$$ 11x + 10 = 14x + 7 $$
$$ 3x =3$$
$$ \Rightarrow x = 1$$
$$\therefore$$ The number $$= 11 \times 1 + 10= 21$$
Question 5
1 / -0

Given that $$\displaystyle \frac {-6p - 9}{3}\, =\, \displaystyle \frac {2p + 9}{5}$$, find the value of $$p$$.

A
$$-4$$

B
$$-2$$

C
$$3$$

D
$$5$$

Solution

Given, $$\displaystyle \frac {-6p - 9}{3}\, =\, \displaystyle \frac {2p + 9}{5}$$
$$\Rightarrow -2p-3=\cfrac {2p + 9}{5}$$
$$\Rightarrow -10p-15=2p+9$$
$$\Rightarrow -12p=24$$
$$\Rightarrow p=-2$$
Question 6
1 / -0

If $$2x + 3 = x - 4,$$ then the value of $$x$$ is

A
$$-4$$

B
$$-7$$

C
$$-9$$

D
$$-10$$

Solution

$${\textbf{Step -1: Solve linnear equation in variable with variable on both sides.}}$$
$${\text{Given}}$$ $$2x + 3 = x - 4$$
$${\text{put x terms on one side and constants on another side.}}$$
$$\Rightarrow$$ $$2x-x=-4-3$$
$$\Rightarrow$$ $$x=-7$$
$${\text{Hence, the value of x is -7.}} $$
$${\textbf{Hence , option B is correct. The value of x is -7.}}$$
Question 7
1 / -0

If the sum of three consecutive even numbers is $$234$$, then the smallest among them is

A
$$76$$

B
$$78$$

C
$$80$$

D
None of these

Solution

Let the three consecutive even numbers be $$2x-2, 2x, 2x+2$$.
We have,
$$(2x - 2) + 2x + (2x + 2) = 234$$
$$\Rightarrow 6x = 234$$
$$\Rightarrow x = 39$$
$$\therefore$$ Least even number is $$ 2x - 2 = 2(39) - 2 = 76$$.
Question 8
1 / -0

$$2n$$ is an even number. What are the odd numbers on each side of it? The sum of two consecutive odd numbers is $$96$$. What are they?

A
$$41,43$$

B
$$57,59$$

C
$$47,49$$

D
$$31,33$$

Solution

Given: Even number $$=2n$$
The odd number preceding $$2n =2n-1$$
The odd number succeeding $$2n=2n+1$$
A.T.Q,
$$2n-1+2n+1=96$$
$$\implies 4n=96$$
$$\implies n=\dfrac{96}{4}=24$$
$$\therefore$$ the consecutive odd numbers are $$2\times 24-1=47$$ and $$2\times 47+1=49$$
They are $$47,49$$
Question 9
1 / -0

$$3x =2x + 20$$
What is the value of the $$x$$?

A
16

B
18

C
20

D
22

Solution

We have, $$3x = 2x + 20$$
$$\Rightarrow$$ $$3x - 2x = 20$$ [Transposing $$2x$$ to LHS]
$$\Rightarrow $$ $$x=20$$
Question 10
1 / -0

A grandfather is ten times older than his grand daughter. He is also $$54$$ years older than her. Find their present ages.

A
The present age of granddaughter is $$6$$ years and that of grandfather is $$60$$ years.

B
The present age of granddaughter is $$8$$ years and that of grandfather is $$80$$ years.

C
The present age of granddaughter is $$7$$ years and that of grandfather is $$70$$ years.

D
The present age of granddaughter is $$9$$ years and that of grandfather is $$90$$ years.

Solution

Let the present age of granddaughter be $$x$$ years.
So, the present age of grandfather is $$10x$$ years.
According to the given condition, we have
$$10x-x=54$$
$$\Rightarrow 9x=54$$
$$ \Rightarrow x=6$$ .... On dividing $$9$$ from both the sides
Hence, the present age of granddaughter is $$6$$ years and that of grandfather is $$60$$ years.

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Re-Attempt Weekly Quiz Competition

Linear Equations in One Variable Test - 32

Result

Linear Equations in One Variable Test - 32

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SHARING IS CARING

Question 1

$$18$$

$$14$$

$$22$$

$$24$$

Solution

Question 2

70

68

72

22

Solution

Question 3

$$446$$

$$561$$

$$682$$

$$862$$

Solution

Question 4

$$65$$

$$43$$

$$32$$

$$21$$

Solution

Question 5

$$-4$$

$$-2$$

$$3$$

$$5$$

Solution

Question 6

$$-4$$

$$-7$$

$$-9$$

$$-10$$

Solution

Question 7

$$76$$

$$78$$

$$80$$

None of these

Solution

Question 8

$$41,43$$

$$57,59$$

$$47,49$$

$$31,33$$

Solution

Question 9

16

18

20

22

Solution

Question 10

The present age of granddaughter is $$6$$ years and that of grandfather is $$60$$ years.

The present age of granddaughter is $$8$$ years and that of grandfather is $$80$$ years.

The present age of granddaughter is $$7$$ years and that of grandfather is $$70$$ years.

The present age of granddaughter is $$9$$ years and that of grandfather is $$90$$ years.

Solution

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