The average weight of three boys P, Q and R is 54 kg, while the average weight…

Concept: When two groups share one common member, adding the two group totals counts that shared member twice. To turn this combined total into the total (and hence the average) of all the distinct members, the shared member's individual value must be known so it can be subtracted out; without it, the combined total cannot be resolved into one unique average.

1. Average of P, Q, R is 54 kg, so P + Q + R = 3 x 54 = 162 kg.

2. Average of Q, S, T is 60 kg, so Q + S + T = 3 x 60 = 180 kg.

3. Adding the two totals: (P + Q + R) + (Q + S + T) = P + 2Q + R + S + T = 162 + 180 = 342 kg.

4. The sum needed for the five distinct boys is P + Q + R + S + T, which equals 342 - Q, since Q was counted twice above.

5. Q's individual weight is not given anywhere in the question, so 342 - Q cannot be reduced to a single number, and neither can the average of the five boys.

Cross-check: Trying different assumed values for Q (say 54 kg or 60 kg) changes the resulting five-boy total each time, confirming the answer genuinely depends on the unknown Q rather than settling to one fixed value.

So, the data given is inadequate to find the average weight of P, Q, R, S and T.