The average weight of Shivshankar, Gopesh, and Reena is 97 kg. The average of Shivshankar and Gopesh is 93 kg, and the average of Gopesh and Reena is 82 kg. What is the weight of Gopesh (in kg)?

Introduction:
When multiple averages over overlapping pairs and a triple are given, add the pair sums and compare with the triple sum to isolate the shared person's value. This uses linear relationships among sums efficiently.

Given Data / Assumptions:
Avg(S, G, R) = 97 ⇒ S + G + R = 291. Avg(S, G) = 93 ⇒ S + G = 186. Avg(G, R) = 82 ⇒ G + R = 164.

Concept / Approach:
Add (S + G) and (G + R) to get S + 2G + R, which equals (S + G + R) + G. Compare with the triple sum to solve for G.

Step-by-Step Solution:
(S + G) + (G + R) = 186 + 164 = 350. But S + 2G + R = (S + G + R) + G = 291 + G. Therefore, 350 = 291 + G ⇒ G = 59.

Verification / Alternative check:
Compute S = 186 − 59 = 127 and R = 164 − 59 = 105. Check: 127 + 59 + 105 = 291 and averages match the given values.

Why Other Options Are Wrong:
72, 56, 63, 61: Substituting any of these for G breaks one or more of the provided average relationships.

Common Pitfalls:
Trying to average the three given averages directly or solving for the wrong variable first. Focus on sums: pair sums vs triple sum lets you isolate G quickly.

Final Answer:
The weight of Gopesh is 59 kg.