The average weight of Somdev, Gurdeep and Ritu together is 85 kg. The average weight of Somdev and Gurdeep together is 79 kg, and the average weight of Gurdeep and Ritu together is 73 kg. What is the weight of Gurdeep (in kilograms)?

Introduction / Context: This question is similar in structure to other average problems with three unknowns and three average relations. We are given the average weight of all three persons (Somdev, Gurdeep and Ritu) and the averages of two-person pairs. We are asked to find Gurdeep's individual weight using simple algebra. Given Data / Assumptions:

• Average weight of Somdev (S), Gurdeep (G) and Ritu (R) together = 85 kg.
• Average weight of Somdev and Gurdeep = 79 kg.
• Average weight of Gurdeep and Ritu = 73 kg.
• We must find G.

Concept / Approach: We convert each average to a sum equation:

• S + G + R = 3 * 85.
• S + G = 2 * 79.
• G + R = 2 * 73.

Then we add and subtract these equations appropriately to isolate G. This gives us a neat solution with minimal computation. Step-by-Step Solution: Step 1: Translate averages into sums. S + G + R = 3 * 85 = 255. S + G = 2 * 79 = 158. G + R = 2 * 73 = 146. Step 2: Add the last two equations. (S + G) + (G + R) = 158 + 146 = 304. Left side becomes S + 2G + R. So S + 2G + R = 304. Step 3: Subtract S + G + R = 255 from this equation. (S + 2G + R) − (S + G + R) = 304 − 255. Left side simplifies to G; right side is 49. Thus, G = 49 kg. Verification / Alternative check: Find S and R to confirm. From S + G = 158 → S = 158 − 49 = 109. From G + R = 146 → R = 146 − 49 = 97. Check the total: S + G + R = 109 + 49 + 97 = 255. Average = 255 / 3 = 85 kg, which matches the given overall average. Why Other Options Are Wrong: If G were 78, 72, 90 or 65, then the derived values of S and R from S + G = 158 and G + R = 146 would not add up to 255, and the average of the three would not be 85. Hence, these choices are inconsistent with at least one of the given relations. Common Pitfalls: Some students may accidentally average the given averages (79 and 73) instead of using them as sums, leading to confusion. Others might miscalculate 2 * 79 or 2 * 73, which changes the equations and yields incorrect results. Final Answer: The weight of Gurdeep is 49 kilograms.