NIMCET 2025 — Reasoning PYQ

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Question

NIMCET 2025 — Reasoning PYQ

NIMCET | Reasoning | 2025

Ten years ago, Ram was twice as old as Shyam. Ten years from now, the ratio of their ages will be 3:2.

What is Ram's present age?

Choose the correct answer:

Explanation

1. Equation from the first condition (Ten years ago):

Ten years ago, their ages were $(R - 10)$ and $(S - 10)$ .

(R - 10) = 2(S - 10)

R - 10 = 2S - 20

R - 2S = -10 \quad \text{--- (Eq. 1)}

2. Equation from the second condition (Ten years from now):

Ten years from now, their ages will be $(R + 10)$ and $(S + 10)$ . The ratio is $3:2$ .

\frac{R + 10}{S + 10} = \frac{3}{2}

2(R + 10) = 3(S + 10)

2R + 20 = 3S + 30

2R - 3S = 10 \quad \text{--- (Eq. 2)}

3. Solving the equations:

Multiply (Eq. 1) by $2$ to align the $R$ terms:

2R - 4S = -20 \quad \text{--- (Eq. 3)}

Subtract (Eq. 3) from (Eq. 2):

(2R - 3S) - (2R - 4S) = 10 - (-20)

-3S + 4S = 10 + 20

S = 30

4. Find Ram's present age ( $R$ ):

Substitute $S = 30$ into (Eq. 1):

R - 2(30) = -10

R - 60 = -10

R = 60 - 10

R = 50

Correct Option: a) 50 years