The present ages of Vivek and Sumit are in the ratio 2 : 3. After 12 years, their ages will be in the ratio 11 : 15. What is Sumit’s current age?

Introduction / Context:
This is a classic age-ratio problem involving present and future ratios. We must convert ratio statements into equations and solve for the scaling factor of the current ages.

Given Data / Assumptions:

• Present ratio (Vivek : Sumit) = 2 : 3.
• After 12 years, ratio becomes 11 : 15.
• Find Sumit’s current age.

Concept / Approach:
If present ages are 2x and 3x, then after 12 years they are (2x + 12) and (3x + 12). Set their ratio to 11 : 15 and solve for x. Then compute Sumit’s age = 3x.

Step-by-Step Solution:
Let Vivek = 2x, Sumit = 3x. (2x + 12) : (3x + 12) = 11 : 15. 15(2x + 12) = 11(3x + 12). 30x + 180 = 33x + 132. 48 = 3x ⇒ x = 16. Sumit’s present age = 3x = 48 years.

Verification / Alternative check:
After 12 years: Vivek = 32 + 12 = 44; Sumit = 48 + 12 = 60; Ratio 44 : 60 reduces to 11 : 15, confirming the result.

Why Other Options Are Wrong:
32 or 42 years do not satisfy the future ratio when checked. 56 years would make the future ratio exceed 11 : 15.

Common Pitfalls:
Forgetting to add 12 to both ages, or simplifying ratios incorrectly. Always check by substituting back into the future ratio condition.

Final Answer:
48 years