Problems on Ages — “A father (Sanyal) is three times his son’s present age. Six years hence, their ages will be in the ratio 5 : 2. Find Sanyal’s present age.”

Introduction / Context:
Parent–child age problems often give a present-time multiple and a future-time ratio. Setting the parent as a multiple of the child’s present age, then applying the future ratio, yields a single unknown variable to solve.

Given Data / Assumptions:

• Let son = s; father (Sanyal) = 3s now.
• After 6 years: (3s + 6) : (s + 6) = 5 : 2.

Concept / Approach:
Cross-multiply to obtain a linear equation in s; compute s and then Sanyal’s age 3s.

Step-by-Step Solution:

Verification / Alternative check:
Six years later: father 60, son 24 ⇒ 60 : 24 = 5 : 2 ✓.

Why Other Options Are Wrong:
48/50/60/45 do not respect both the present multiple and the 5:2 future ratio when paired with a consistent son’s age.

Common Pitfalls:
Forgetting to add 6 to both ages; setting father = 3(s + 6) instead of 3s + 6 (the multiple applies to present ages only).

Final Answer:
54 years