NIMCET 2022 — Reasoning PYQ

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Question

NIMCET 2022 — Reasoning PYQ

NIMCET | Reasoning | 2022

A person’s present age two-fifth of the age of his mother. After 8 yr, he will be one-half of the age of the age of his mother. What is the present age of the mother?

Choose the correct answer:

Explanation

Solution

To solve this, let's define the present ages:

Let the mother's present age be $x$ .
The person's present age is therefore $\frac{2}{5} x$ .

1. Set up the equation for age after 8 years:

After $8$ years:

Mother's age will be $x + 8$ .
Person's age will be $\frac{2}{5} x + 8$ .

According to the problem, after $8$ years, the person's age will be half of the mother's age:

$\frac{2}{5} x + 8 = \frac{1}{2} (x + 8)$

2. Solve for $x$ :

Multiply both sides by $10$ to clear the fractions:

$10 (\frac{2}{5} x + 8) = 10 (\frac{1}{2} (x + 8))$

$4 x + 80 = 5 (x + 8)$

$4 x + 80 = 5 x + 40$

Rearrange to solve for $x$ :

$80 - 40 = 5 x - 4 x$

$x = 40$

The mother's present age is $40$ years.

Correct Option: A) $40$ yr