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

Introduction / Context:
Here we have two time-shifted multiplicative relations between the same two people. Represent the present ages with variables and translate each statement into an equation at the appropriate time point; solving the system gives Ashok’s current age.

Given Data / Assumptions:

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

Concept / Approach:
Convert both conditions to present-age equations and solve simultaneously.

Step-by-Step Solution:

Verification / Alternative check:
Five years ago: Ashok 10, Mother from (1) ⇒ y = 35 ⇒ 35 = 3 * 10 + 5? Actually condition is y − 5 = 3(x − 5) ⇒ 30 = 3 * 10 ✓; Five years hence: Ashok 20, Mother 40 ⇒ 40 = 2 * 20 ✓.

Why Other Options Are Wrong:
10/20/25/18 break one of the time-shifted multiplicative conditions when checked in both directions.

Common Pitfalls:
Applying the multiplier to present ages (3x) instead of to the shifted age (x − 5); forgetting to add/subtract 5 to both ages for the same time frame.

Final Answer:
15 years