Proportional ages then and now: Neela is now three times as old as her daughter Leela. Ten years ago, Neela was five times as old as Leela. What is Leela’s present age?

Introduction / Context:
Present and past multiplicative relations between ages form a solvable system. Let present ages be in a simple ratio, then use the past condition to fix the scale.

Given Data / Assumptions:

• N = 3L (now).
• Ten years ago: N − 10 = 5(L − 10).

Concept / Approach:
Substitute N = 3L into the ten-years-ago equation and solve for L.

Step-by-Step Solution:
1) 3L − 10 = 5L − 50.2) Move terms: 40 = 2L ⇒ L = 20.3) Therefore Leela is 20 years old now (Neela is 60).

Verification / Alternative check:
Ten years ago: 50 vs 10 → 5×. Now: 60 vs 20 → 3×. Consistent.

Why Other Options Are Wrong:
They break either the present 3× or the past 5× condition.

Common Pitfalls:
Forgetting both ages decrease by 10 simultaneously when moving to “ten years ago.”

Final Answer:
20