The average weight of P, Q and R together is 47 kg. The average weight of P and Q together is 32.5 kg, and the average weight of Q and R together is 48.5 kg. What is the weight of Q (in kilograms)?

Introduction / Context: This is an average and linear-equation problem involving three people P, Q and R. We are given the average of all three together and the averages of two pairs: (P, Q) and (Q, R). Using this information, we can form a system of equations and solve for the individual weight of Q. Given Data / Assumptions:

• Average weight of P, Q, R = 47 kg.
• Average weight of P and Q = 32.5 kg.
• Average weight of Q and R = 48.5 kg.
• Let weights be P, Q, R in kg.
• We must find Q.

Concept / Approach: We convert the averages into total-weight equations by multiplying by the number of people in each group:

• P + Q + R = 3 * 47.
• P + Q = 2 * 32.5.
• Q + R = 2 * 48.5.

Then we use these equations to eliminate P and R and isolate Q. It is straightforward algebra with careful arithmetic. Step-by-Step Solution: Step 1: Translate averages into sums. P + Q + R = 3 * 47 = 141. P + Q = 2 * 32.5 = 65. Q + R = 2 * 48.5 = 97. Step 2: Add the equations for P + Q and Q + R. (P + Q) + (Q + R) = 65 + 97. Left side is P + 2Q + R; right side is 162. So P + 2Q + R = 162. Step 3: Subtract P + Q + R = 141 from this equation. (P + 2Q + R) − (P + Q + R) = 162 − 141. Left side simplifies to Q; right side is 21. Hence Q = 21 kg. Verification / Alternative check: From P + Q = 65, we get P = 65 − Q = 65 − 21 = 44. From Q + R = 97, we get R = 97 − Q = 97 − 21 = 76. Check the total: P + Q + R = 44 + 21 + 76 = 141. Average of all three = 141 / 3 = 47 kg, matching the given average. Why Other Options Are Wrong: If Q were 25, 29, 33 or 31, the corresponding values of P and R computed from P + Q = 65 and Q + R = 97 would not give the correct total 141. Thus, those alternatives violate at least one of the original average conditions. Common Pitfalls: A common mistake is to incorrectly double the averages (e.g., miscomputing 2 * 32.5 as 64 or 66 instead of 65). Another error is adding or subtracting the equations incorrectly, which can yield wrong values for Q. Final Answer: The weight of Q is 21 kilograms.