Question

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. 50
• B. 60
• C. 40
• D. 70

Hint:

When solving age-related problems, set up equations based on given relationships and solve step-by-step.

Answer 1

The Correct Option is A

Let Ram's present age be \( R \) and Shyam's present age be \( S \). From the problem: - Ten years ago, Ram was twice as old as Shyam: \[ R - 10 = 2(S - 10) \] - Ten years from now, the ratio of their ages will be 3:2: \[ \frac{R + 10}{S + 10} = \frac{3}{2} \] Solving the first equation: \[ R - 10 = 2(S - 10) $\Rightarrow$ R - 10 = 2S - 20 $\Rightarrow$ R = 2S - 10 \] Substitute this into the second equation: \[ \frac{(2S - 10) + 10}{S + 10} = \frac{3}{2} $\Rightarrow$ \frac{2S}{S + 10} = \frac{3}{2} \] Cross-multiply: \[ 4S = 3(S + 10) $\Rightarrow$ 4S = 3S + 30 $\Rightarrow$ S = 30 \] Substitute \( S = 30 \) into the equation for \( R \): \[ R = 2(30) - 10 = 60 - 10 = 50 \] Thus, Ram's present age is \( \boxed{50} \).