Five years ago, the average age of Ram and Shyam was 20 years. Now, the average age of Ram, Shyam, and Mohan is 30 years. What will be Mohan’s age 10 years hence?

Introduction:
Family or group age problems are most cleanly handled by converting averages to totals and then tracking how totals change over time as members age or new members are added.

Given Data / Assumptions:

• 5 years ago: average of (Ram, Shyam) = 20 ⇒ past total = 40.
• Now: average of (Ram, Shyam, Mohan) = 30 ⇒ current total = 90.
• Aging is linear: each of Ram and Shyam gained 5 years since the earlier snapshot.

Concept / Approach:
Convert both averages to totals and reconcile. Compute Ram + Shyam now, then subtract from the current 3-person total to isolate Mohan’s present age. Add 10 to project 10 years ahead.

Step-by-Step Solution:

Verification / Alternative check:
Present averages: (Ram + Shyam)/2 is not required; totals are sufficient. All values remain consistent with the provided averages after back-substitution.

Why Other Options Are Wrong:
45, 49, and 60 years do not follow from Mohan’s present age of 40. 40 years is Mohan’s current age, not his age 10 years later.

Common Pitfalls:
Averaging the given averages or forgetting that both Ram and Shyam aged for 5 years each, i.e., +10 total years for the pair.

Final Answer:
50 years