The average weight of three persons P, Q and R is 71 kg. If the average weight of P and Q together is 66 kg and the average weight of Q and R together is 76.5 kg, what is the weight of Q in kilograms?

Introduction / Context:
This final question in the set is another averages and linear equations problem involving weights of three people. You know the average of all three, plus the averages of two different pairs. The goal is to determine the individual weight of Q. This structure mirrors many common aptitude questions where overlapping group averages lead to simple algebraic equations.

Given Data / Assumptions:
- Persons are P, Q and R.
- Average weight of P, Q and R together = 71 kg.
- Average weight of P and Q together = 66 kg.
- Average weight of Q and R together = 76.5 kg.
- We must find the weight of Q in kilograms.

Concept / Approach:
As in similar problems, we first convert each average to a total weight. We find totals for P + Q + R, P + Q and Q + R. By subtracting P + Q from the total, we get R, and by subtracting Q + R from the total we get P. Once we know P and R, we combine the relevant totals to isolate Q. The method is clean and uses basic algebra and arithmetic only.

Step-by-Step Solution:
Step 1: Total weight of P, Q and R = 3 * 71 = 213 kg.Step 2: Total weight of P and Q = 2 * 66 = 132 kg.Step 3: Total weight of Q and R = 2 * 76.5 = 153 kg.Step 4: From step 1 and step 2, compute R: R = (P + Q + R) - (P + Q) = 213 - 132 = 81 kg.Step 5: From step 1 and step 3, compute P: P = (P + Q + R) - (Q + R) = 213 - 153 = 60 kg.Step 6: Now use P + Q = 132 to find Q: 60 + Q = 132.Step 7: So Q = 132 - 60 = 72 kg.Step 8: Therefore, the weight of Q is 72 kg.

Verification / Alternative check:
Check all given averages. With P = 60, Q = 72 and R = 81, the total P + Q + R = 60 + 72 + 81 = 213, so the overall average is 213 / 3 = 71 kg, matching the first condition. For P and Q, total is 60 + 72 = 132 and average is 132 / 2 = 66 kg, matching the second condition. For Q and R, total is 72 + 81 = 153 and average is 153 / 2 = 76.5 kg, matching the third condition. All three given averages are consistent with these weights, confirming the answer.

Why Other Options Are Wrong:
If Q were 60, 75, 69 or 81, then at least one of the three average conditions would fail. For example, if Q were 75 and P + Q = 132, then P would be 57, and this combined with a suitable R would not satisfy the overall average of 71 and the given Q + R average at the same time. Only Q = 72 kg works with a consistent set of values for P and R.

Common Pitfalls:
Some learners attempt to guess Q without systematically converting averages to totals. Others mix up which totals correspond to which pairs. The safest approach is to write down the three equations for P + Q + R, P + Q and Q + R, express P and R in terms of these totals and then solve step by step. Finally, always verify your result by checking all given averages.

Final Answer:
The weight of Q is 72 kg.