Problems on Ages — “Five years ago, Ashu’s mother was 3 times Ashu’s age. Five years from now she will be twice Ashu’s age. Find Ashu’s present age.”

Introduction / Context:This problem mirrors the earlier two-equation pattern with past and future multiplicative age relations. Represent present ages with variables and translate the time-shifted statements into equations to solve cleanly.

Given Data / Assumptions:

• Let Ashu = x, Mother = y (present ages).
• Five years ago: y − 5 = 3(x − 5).
• Five years hence: y + 5 = 2(x + 5).

Concept / Approach:Convert to present-age equations and solve simultaneously for x.

Step-by-Step Solution:

Verification / Alternative check:Five years ago Ashu 10, Mother 30 ⇒ 30 = 3 * 10 ✓; in five years Ashu 20, Mother 40 ⇒ 40 = 2 * 20 ✓.

Why Other Options Are Wrong:10/12/20/35 violate at least one of the two time-shifted multiplicative conditions.

Common Pitfalls:Applying the multiplier to current ages directly; forgetting to shift both ages by the same number of years when moving to past or future.

Final Answer:15 years