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?

31

$\text{Average weight of P, Q, and R} = 45\text{ kg}$

$\text{Total weight (P + Q + R)} = 45 \times 3 = 135\text{ kg} \quad \text{--- (Equation 1)}$

$\text{Average weight of P and Q} = 40\text{ kg}$

$\text{Total weight (P + Q)} = 40 \times 2 = 80\text{ kg} \quad \text{--- (Equation 2)}$

$\text{Average weight of Q and R} = 43\text{ kg}$

$\text{Total weight (Q + R)} = 43 \times 2 = 86\text{ kg} \quad \text{--- (Equation 3)}$

If we add Equation 2 and Equation 3 together, Q is counted twice:

$\text{(P + Q)} + \text{(Q + R)} = 80 + 86$

$\text{P + 2Q + R} = 166\text{ kg}$

Now, subtract the total weight of all three (Equation 1) from this sum to isolate Q:

$\text{Weight of Q} = (\text{P + 2Q + R}) - (\text{P + Q + R})$

$\text{Weight of Q} = 166 - 135 = 31\text{ kg}$