### The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

A. 17 kg

B. 20 kg

C. 26 kg

D. 31 kg

Let A, B, C represent their respective weights. Then, we have : $\begin{array}{l}\text{A + B + C = (45 × 3) = 135…..(i)}\\ \text{A + B = (40 × 2) = 80…..(ii)}\\ \text{B + C = (43 × 2) = 86…..(iii)}\\ \text{Adding (ii) and (iii), we get:}\\ \text{A + 2B + C = 166…..(iv)}\end{array}$ Subtracting (i) from (iv), we get: B = 31 ∴ B’s weight = 31 kg