Linear Equations(10th Grade > Mathematics ) Questions and answers for exam Preparation

10th Grade > Mathematics

LINEAR EQUATIONS MCQs

Linear Equations In One Variable, Linear Equations In Two Variables, Pair Of Linear Equations In Two Variables (8th, 9th And 10th Grade)

Total Questions : 74 | Page 8 of 8 pages

Question 71. The value of the variable after solving the equation 2x + 3 = 3x + 2 is
___.

Discuss Question

:
In the given equation, x is the variable (whose value has to be found)
2x + 3 = 3x + 2
3x - 2x = 3 - 2
x = 1

Question 72. The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, then the new number becomes

\frac{3}{2}

. Find the original number.

Discuss Question

Answer: Option A. -> 811
:
A
Let the numerator of a rational number be

x

.
Then the denominator of a rational number would be

(x + 3)

.
When the numerator is increased by

7

, it becomes

(x + 7)

When the denominator is decreased by 1, it becomes

\Rightarrow x + 3 - 1 = x + 2

The new number formed

= \frac{3}{2}

So, \frac{(x + 7)}{(x + 2)} = \frac{3}{2} 2 x + 14 = 3 x + 6 3 x - 2 x = 14 - 6 x = 8

∴

Numerator,

x = 8

Denominator,

x + 3 = 8 + 3 = 11

Hence, the original rational numberis

\frac{8}{11}

Question 73. The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 4 : 5. The present age of Pratik would be
___ years.

Discuss Question

:
Let the present age of Pratik be 2x and Arjun be 3x.
4 years from now, Pratik 's age = 2x + 4 and Arjun 's age = 3x + 4
Given that,

\frac{2 x + 4}{3 x + 4} = \frac{4}{5}

⟹ 10 x + 20 = 12 x + 16

Thus,

2 x = 4 ⟹ x = 2

Pratik's present age is

2 x = 4

Question 74. If the sum of three consecutive multiples of 4 is 444, then these multiples are 144, 148, 152.

True
False
710
25

Discuss Question

Answer: Option A. -> True
:
A
Let us assume the first multiple of 4 as 4x. Hence,the next two multiples are4x + 4 and 4x + 8
According to the question,