Recover past age from present ratio and a future value: Tarun : Varun = 3 : 7 (present). Four years from now, Varun will be 39. What was Tarun’s age 4 years ago?

Introduction / Context:One person’s future age determines both present ages through the given present ratio. Once present ages are known, subtract 4 to get Tarun’s age 4 years ago.

Given Data / Assumptions:

• Present ratio Tarun : Varun = 3 : 7
• Varun in 4 years = 39 ⇒ Varun now = 35

Concept / Approach:Use the ratio to derive Tarun’s present age from Varun’s present age. Then shift back 4 years to answer the question.

Step-by-Step Solution:

Verification / Alternative check:Check ratio now: 15 : 35 = 3 : 7 ✓. Future value for Varun matches 39 after 4 years.

Why Other Options Are Wrong:12, 13, 19 do not equal the calculated 11 years.

Common Pitfalls:Applying the ratio to future ages; the ratio given is explicitly for present ages.

Final Answer:11 yr