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?
- (a) A
- (b) B ✓ UPSC's answer
- (c) C
- (d) D
Why the answer is (b)
• Write the incomes as A, B, C and D.
• "A earns half as much as B and D together" gives B + D = 2A.
• "A + C equals B + D" then gives A + C = 2A, so C = A.
• "A + B is more than C + D" becomes A + B > A + D, so B > D.
• Since B + D = 2A and B > D, B is above the average of B and D, which is A; so B > A = C > D.
• B has the highest income, option (b).
Why the other options are wrong
- (a) A
- A equals C and is less than B, because B + D = 2A with B > D.
- (c) C
- C equals A, which is less than B.
- (d) D
- D is the smallest: D < A because B + D = 2A and B > D.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.