Question

Five years ago. Ramu was thrice as old as Somu and ten years later, Ramu will be twice as old as Somu. Then the present ages of Ramu and Somu respectively are

• A. 35.20
• B. 20.35
• C. 20.50
• D. 50.20

Answer 1

The Correct Option is D

Step 1: Define variables.

Let the present age of Ramu be \( R \) and the present age of Somu be \( S \).

Step 2: Translate the conditions into equations.

• Five years ago, Ramu was thrice as old as Somu:
• Ten years later, Ramu will be twice as old as Somu:

Step 3: Simplify the equations.

From the first equation:

\[ R - 5 = 3S - 15 \implies R = 3S - 10. \]

From the second equation:

\[ R + 10 = 2S + 20 \implies R = 2S + 10. \]

Step 4: Solve the system of equations.

Set the two expressions for \( R \) equal to each other:

\[ 3S - 10 = 2S + 10. \]

Simplify:

\[ S = 20. \]

Substitute \( S = 20 \) into \( R = 3S - 10 \):

\[ R = 3(20) - 10 = 60 - 10 = 50. \]

Final Answer: The present ages of Ramu and Somu are \( \mathbf{50 \text{ and } 20} \), which corresponds to option \( \mathbf{(4)} \).