Problems on Ages — “Present ratio Gopal : Madhawa = 4 : 3. After 6 years, Gopal will be 26 years old. Find Madhawa’s present age.”

Introduction / Context:
One person’s future age is given along with a present-time ratio. Use the future age to back out that person’s present age, then apply the ratio to compute the other person’s present age.

Given Data / Assumptions:

• Now: Gopal : Madhawa = 4 : 3 ⇒ let G = 4k, M = 3k.
• After 6 years: Gopal = 26 ⇒ G + 6 = 26.

Concept / Approach:
From G + 6 = 26 get G = 20. Then find k = 20/4 = 5, and M = 3k.

Step-by-Step Solution:

Verification / Alternative check:
Check ratio now: 20 : 15 = 4 : 3 ✓.

Why Other Options Are Wrong:
12/17/19.5/21 years would break the 4:3 present ratio given G = 20.

Common Pitfalls:
Forgetting to subtract the 6 years to get the present age; incorrectly distributing the ratio before determining k.

Final Answer:
15 years