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?

(a) B and D together weigh less than the total weight of P and Q.
(b) P and Q together weigh more than the total weight of A and C. ✓ UPSC's answer
(c) P weighs more than Q.
(d) Q weighs more than P.

Why the answer is (b)

['- From the equations A + C = 6 and A + B + C + D = 17, we can deduce that B + D = 17 - 6 = 11.', '- From the equations P + Q + S + D = 15 and P + Q + R + B = 17, and given P = R and Q = S, we substitute to get P + Q + Q + D = 15 and P + Q + P + B = 17.', '- Adding these two new equations gives 2P + 2Q + B + D = 32. Since B + D = 11, we have 2(P + Q) + 11 = 32, which simplifies to 2(P + Q) = 21, so P + Q = 10.5.', '- Comparing the total weight of P and Q (10.5 kg) with the total weight of A and C (6 kg), we see that 10.5 > 6.', '- Therefore, P and Q together weigh more than the total weight of A and C, making option (b) correct.']

Why the other options are wrong

(a) B and D together weigh less than the total weight of P and Q.: B and D together weigh 11 kg, which is more than the total weight of P and Q (10.5 kg).
(c) P weighs more than Q.: The given equations and conditions do not provide enough information to determine the individual weights of P and Q, only their sum.
(d) Q weighs more than P.: The given equations and conditions do not provide enough information to determine the individual weights of P and Q, only their sum.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.