Vaibhav is elder by 3 years to Rohit. After 10 years Vaibhav will be thrice…

Concept:

In an ages problem, translate each word statement into a linear equation in the persons' present ages. A phrase like "after t years a person's age becomes k times the present age" means (present age) + t = k × (present age), and "A is elder by d years to B" means A = B + d. Solving the resulting equations gives every present age.

Application:

1. Let Vaibhav's present age be V and Rohit's present age be R. The phrase "Vaibhav is elder by 3 years to Rohit" gives V = R + 3.

2. "After 10 years Vaibhav will be thrice his present age" gives V + 10 = 3V, so 2V = 10 and V = 5.

3. "Rohit will be six times his present age" gives R + 10 = 6R, so 5R = 10 and R = 2.

4. Hence Rohit's present age is 2 years.

Cross-check:

With V = 5 and R = 2, the gap V − R = 5 − 2 = 3, matching "elder by 3 years". After 10 years Vaibhav is 5 + 10 = 15 = 3 × 5, and Rohit is 2 + 10 = 12 = 6 × 2. All three conditions hold, so R = 2 years.