Pairwise averages: If (Dinesh + Mahesh)/2 = 16, (Mahesh + Rahul)/2 = 13, and (Dinesh + Rahul)/2 = 14, what is Mahesh’s age?

Introduction / Context:
With three pairwise averages, linear equations allow recovery of each individual age. Adding and subtracting strategically eliminates variables.

Given Data / Assumptions:

• (D + M)/2 = 16 ⇒ D + M = 32
• (M + R)/2 = 13 ⇒ M + R = 26
• (D + R)/2 = 14 ⇒ D + R = 28

Concept / Approach:
Add equations to collect terms and compare with a third to isolate one variable. Here, summing the first two and subtracting the third isolates M.

Step-by-Step Solution:

Verification / Alternative check:
Compute D = 32 - M = 17 and R = 26 - M = 11; check D + R = 28. Works.

Why Other Options Are Wrong:

• 20 yr, 58 yr, 16 yr: Inconsistent with the three equations.

Common Pitfalls:
Trying to average the three averages directly without solving the system or mishandling subtraction.

Final Answer: