The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given :
A + B + C + D = 17
A + C = 6
P + Q + S + D = 15
P + Q + R + B = 17
P = R and Q = S

Which one of the following statements is correct?

Correct Option: (b) P and Q together weigh more than the total weight of A and C.

Let's analyze the given equations for weights: 1) A + B + C + D = 17, 2) A + C = 6, 3) P + Q + S + D = 15, 4) P + Q + R + B = 17, 5) P = R and Q = S. From (1) and (2): (A + C) + B + D = 17 => 6 + B + D = 17 => B + D = 11. Using (5) in (3): P + Q + Q + D = 15 => P + 2Q + D = 15. Using (5) in (4): P + Q + P + B = 17 => 2P + Q + B = 17. Adding the two modified equations: (P + 2Q + D) + (2P + Q + B) = 15 + 17 => 3P + 3Q + B + D = 32. Since B + D = 11, substitute it: 3P + 3Q + 11 = 32 => 3P + 3Q = 21 => P + Q = 7. Since P + Q = 7, the total weight of P and Q is 7. Comparing this with A and C: A + C = 6, so P + Q (7) is greater than A + C (6). Thus, P and Q together weigh more than the total weight of A and C.