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 A + B + C + D = 17 and A + C = 6: B + D = 11.
• Put R = P and S = Q: P + 2Q + D = 15 and 2P + Q + B = 17.
• Add them: 3P + 3Q + (B + D) = 32, so 3(P + Q) = 21 and P + Q = 7.
• P + Q = 7 is more than A + C = 6, so (b) is correct. (a) is false because B + D = 11 is more than 7; P and Q individually cannot be fixed, so (c) and (d) cannot be asserted.
Why the other options are wrong
- (a) B and D together weigh less than the total weight of P and Q.
- B + D = 11 kg, which is more than P + Q = 7 kg.
- (c) P weighs more than Q.
- Only P + Q = 7 is fixed; P and Q individually are not determined.
- (d) Q weighs more than P.
- Only P + Q = 7 is fixed; P and Q individually are not determined.
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.