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UPSC CSE 2026 · PYQ · Linear Equations / Algebra · medium

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?

  1. A.B and D together weigh less than the total weight of P and Q.
  2. B.P and Q together weigh more than the total weight of A and C.✓ Correct
  3. C.P weighs more than Q.
  4. D.Q weighs more than P.

Explanation

From A+B+C+D=17 and A+C=6, we get B+D=11. From P+Q+S+D=15 with Q=S: P+2Q+D=15. From P+Q+R+B=17 with P=R: 2P+Q+B=17. Adding: 3P+3Q+B+D=32, so 3(P+Q)+11=32, hence P+Q=7. Check option (a): B+D=11, P+Q=7, so B+D > P+Q, statement (a) is false. Option (b): P+Q=7, A+C=6, so P+Q > A+C, TRUE. Options (c) and (d) cannot be determined uniquely from given equations since individual P and Q values aren't fixed. Hence (b) is correct.
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