Question 76

Logical Reasoning Age Easy

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?

(A) 60
(B) 40
(C) 50
(D) 70
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\[ \textbf{Given:} \] Let Ram's present age be \( R \) and Shyam's present age be \( S \). \[ \text{Ten years ago: } R - 10 = 2(S - 10) \] \[ R - 10 = 2S - 20 \quad \Rightarrow \quad R = 2S - 10 \quad (1) \] \[ \text{Ten years from now: } \frac{R + 10}{S + 10} = \frac{3}{2} \] \[ 2(R + 10) = 3(S + 10) \] \[ 2R + 20 = 3S + 30 \quad \Rightarrow \quad 2R = 3S + 10 \quad (2) \] \[ \textbf{Substitute (1) into (2):} \] \[ 2(2S - 10) = 3S + 10 \] \[ 4S - 20 = 3S + 10 \] \[ S = 30 \] \[ \text{From (1): } R = 2(30) - 10 = 50 \] \[ \boxed{ \text{Ram's present age is 50 years.} } \]

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