P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A is greater than B.
In this context, which of the following statements is correct?
Answer & explanation
Answer: (d) None of the above can be concluded with certainty.
P − Q = 0.15B − 0.10A, and its sign depends on how much bigger A is than B. If A is less than 1.5 times B, P is larger; if more, Q is larger; at exactly 1.5 times they are equal. So nothing can be concluded.
- P − Q = (0.40A + 0.65B) − (0.50A + 0.50B) = 0.15B − 0.10A.
- P > Q when 0.15B > 0.10A, i.e. A < 1.5B; Q > P when A > 1.5B; P = Q when A = 1.5B.
- A > B allows all three: A = 1.2, B = 1 gives P > Q; A = 3, B = 1 gives Q > P; A = 1.5, B = 1 gives P = Q.
- So the comparison cannot be fixed.
Remember · Subtract the two expressions and study the sign; if it depends on a ratio the question does not fix, the answer is 'cannot be determined'.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·