Average ages across two and three persons with time shift: 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. Find Mohan’s age 10 years from now.

Introduction / Context:
Average-based age problems are solved by converting averages into sums and then using time shifts to adjust sums appropriately. The goal is to isolate the third person’s present age, then push it forward.

Given Data / Assumptions:

• 5 years ago: average(Ram, Shyam) = 20 ⇒ sum then = 40.
• Therefore, sum now for Ram and Shyam = 40 + 2×5 = 50.
• Now: average(Ram, Shyam, Mohan) = 30 ⇒ total now = 90.

Concept / Approach:
Compute present sum of the two from their past average; subtract from the current total of three to find Mohan’s present age; then add 10 years.

Step-by-Step Solution:
1) Present sum (Ram + Shyam) = 50.2) Present sum (Ram + Shyam + Mohan) = 90.3) Mohan now = 90 − 50 = 40.4) Mohan after 10 years = 50.

Verification / Alternative check:
Back-checking: If Mohan is 40 now, the current average of the three is (50 + 40) / 3 = 90/3 = 30, matching the statement.

Why Other Options Are Wrong:

• 45/35/55/40 do not correspond to “Mohan 10 years hence” based on consistent sums.

Common Pitfalls:
Forgetting to add 10 years to the two-person sum when moving forward from “5 years ago” or misinterpreting average as ratio can cause mistakes.

Final Answer:
50 years