The average weight of P, Q and R 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 problem illustrates how to use multiple average equations to find individual values. You are given averages for triples and pairs of people and must extract the weight of a single person.

Given Data / Assumptions:
- The average weight of P, Q and R is 47 kg.
- The average weight of P and Q is 32.5 kg.
- The average weight of Q and R is 48.5 kg.
- We want the weight of Q alone.

Concept / Approach:
We convert each average into a total sum equation. From the first average we get P + Q + R. From the second we get P + Q, and from the third we get Q + R. Using these, we can find R and then Q by simple subtraction.

Step-by-Step Solution:
Step 1: From the average of P, Q and R: (P + Q + R) / 3 = 47, so P + Q + R = 47 * 3 = 141. Step 2: From the average of P and Q: (P + Q) / 2 = 32.5, so P + Q = 32.5 * 2 = 65. Step 3: From the average of Q and R: (Q + R) / 2 = 48.5, so Q + R = 48.5 * 2 = 97. Step 4: Use P + Q + R = 141 and P + Q = 65 to find R: R = 141 - 65 = 76. Step 5: Use Q + R = 97 and R = 76 to get Q: Q = 97 - 76. Step 6: Compute Q = 21 kg.

Verification / Alternative check:
Check all equations. With Q = 21 and R = 76, Q + R = 97, so their average is 48.5. To find P, use P + Q = 65, giving P = 44. Then P + Q + R = 44 + 21 + 76 = 141, whose average is 47. All conditions are satisfied.

Why Other Options Are Wrong:
- Option 25: If Q = 25, the equations for P + Q and Q + R would not match the given averages.

- Option 29: This would force inconsistent values for P and R compared with the given combined totals.

- Option 33: Again, this value would break at least one of the three average relationships provided in the statement.

Common Pitfalls:
Some learners try to solve directly with three variables without first using the simplest subtractions. Others mis-multiply the averages when converting to totals. Always check units, multiply correctly, and use subtraction carefully to isolate each variable step by step.

Final Answer:
The weight of Q is 21 kg.