The sum of income of A and B is more than that of C and D taken together. The sum of income of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the income of B and D. Whose income is the highest?
Answer & explanation
Answer: (b) B
A is half of B + D, and A + C equals B + D, so C = A. Then A + B > C + D gives B > D, and since A is the average of B and D, B is above A. B has the highest income.
- A = (B + D)/2, so B + D = 2A.
- A + C = B + D = 2A, so C = A.
- A + B > C + D becomes A + B > A + D, so B > D.
- A is the average of B and D with B > D, so B > A > D. With C = A, the order is B > A = C > D.
- B has the highest income.
Remember · Turn each sentence into an equation or inequality and substitute; one equality (here C = A) usually unlocks the ranking.
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). ·