The present ages of Mohan and Sohan are in the ratio 3 : 4. Four years ago, their ages were in the ratio 5 : 7. Find the present ages of Mohan and Sohan (in years).

Introduction / Context:
When two age ratios are given at different times, we can convert both into equations in the present ages and solve for exact values. This checks consistency across time shifts.

Given Data / Assumptions:

• Present ratio: Mohan : Sohan = 3 : 4 ⇒ Mohan = 3k, Sohan = 4k.
• Four years ago: (3k − 4) : (4k − 4) = 5 : 7.
• All ages are positive integers (typical ages problems).

Concept / Approach:
Cross-multiply the four-years-ago ratio to produce a linear equation in k, solve for k, then compute both present ages as 3k and 4k. Finally, validate the four-years-ago ratio for correctness.

Step-by-Step Solution:

Verification / Alternative check:
Four years ago: 20 : 28 = 5 : 7, which matches the given ratio exactly.

Why Other Options Are Wrong:
20, 30 and 25, 30 fail the four-years-ago ratio test when you subtract 4 years from each age and compare 5 : 7.

Common Pitfalls:
Forgetting to subtract 4 years from both ages when forming the past ratio; attempting to scale the ratio instead of solving for actual ages via k.

Final Answer:
24 years, 32 years.