Past 3× and future 2× around today: Five years ago Mayank's mother was three times as old as Mayank. Five years from now she will be twice his age. What is Mayank's present age?

Introduction / Context:
Two symmetric time conditions (−5 and +5) precisely fix the present ages. Translate to equations and solve.

Given Data / Assumptions:

• M = mother's present age; m = Mayank's present age.
• Five years ago: M − 5 = 3(m − 5).
• Five years from now: M + 5 = 2(m + 5).

Concept / Approach:
Solve the pair by expressing M from both equations and equating them.

Step-by-Step Solution:
1) From past: M = 3m − 10.2) From future: M = 2m + 5.3) Equate: 3m − 10 = 2m + 5 ⇒ m = 15.4) Then M = 2m + 5 = 35.

Verification / Alternative check:
Five years ago: 30 vs 10 → 3×. In five years: 40 vs 20 → 2×. Both conditions hold.

Why Other Options Are Wrong:
They fail one of the two multiplicative checks upon substitution.

Common Pitfalls:
Mishandling the ±5 shift on both ages; both change simultaneously.

Final Answer:
15 years