The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

Question: The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

Solution:
Let
P, Q, R represent their respective weights. Then, we have:
P + Q + R = (45 × 3) = 135 ........ (i)
P + Q = (40 × 2) = 80 ....... (ii)
Q + R = (43 × 2) = 86 ....... (iii)

Adding (ii) and (iii), we get: P + 2Q + R = 166 ...... (iv)
Subtracting (i) from (iv), we get: Q = 31