Pairwise averages of three people: If avg(Rakesh, Mohan) = 15, avg(Mohan, Ramesh) = 12, and avg(Rakesh, Ramesh) = 13, find Mohan’s age.

Introduction / Context:We are given three pairwise averages among Rakesh (Rk), Mohan (Mo), and Ramesh (Ra). Converting to pairwise sums allows elimination and solution for an individual age directly.

Given Data / Assumptions:

• Rk + Mo = 30
• Mo + Ra = 24
• Rk + Ra = 26

Concept / Approach:Add the first two equations to obtain Rk + 2Mo + Ra. Then substitute Rk + Ra from the third equation to isolate Mo.

Step-by-Step Solution:

Verification / Alternative check:Compute individuals: From Rk + Mo = 30, Rk = 16; from Mo + Ra = 24, Ra = 10. Check Rk + Ra = 26, consistent.

Why Other Options Are Wrong:

• 16, 13, 12, 15: do not satisfy all three pairwise sums simultaneously.

Common Pitfalls:Attempting to solve using three variables directly without first converting to pairwise sums and applying elimination succinctly.

Final Answer:14