Ages (two time-slices with ratios): Two years ago, Ram : Mohan = 3 : 2. At present, Ram : Mohan = 7 : 5. Find their present ages.

Introduction / Context:
This problem gives ratios at two different time points, which is neatly handled by parameterizing the earlier ages and then advancing each by the same elapsed time.

Given Data / Assumptions:

• Two years ago: (R − 2) : (M − 2) = 3 : 2.
• Now: R : M = 7 : 5.

Concept / Approach:
Let R − 2 = 3k and M − 2 = 2k. Then R = 3k + 2, M = 2k + 2. Impose the present ratio to solve for k.

Step-by-Step Solution:

Verification / Alternative check:
Two years ago they were 12 and 8, which reduce to 3 : 2; now they are 14 and 10 → 7 : 5.

Why Other Options Are Wrong:
They violate one of the two ratio constraints when checked.

Common Pitfalls:
Forgetting to add the same 2 years to both persons, or swapping roles of Ram and Mohan when mapping ratios.

Final Answer:
14 years, 10 years