A person P asks one of his three friends X as to how much money he had. X replied, "If Y gives me ₹ 40, then Y will have half of as much as Z, but if Z gives me ₹ 40, then three of us will have equal amount." What is the total amount of money that X, Y and Z have ?
- (a) ₹ 420
- (b) ₹ 360 ✓ UPSC's answer
- (c) ₹ 300
- (d) ₹ 270
Why the answer is (b)
• If Z gives X ₹40, all three have equal amounts: X + 40 = Y = Z − 40. So Y = X + 40 and Z = X + 80.
• If Y gives X ₹40, Y has half of Z: Y − 40 = Z ÷ 2, i.e. X = (X + 80) ÷ 2, so X = 80.
• Then Y = 120 and Z = 160, and the total is 80 + 120 + 160 = ₹360 — option (b).
• Check: after Y gives 40, Y has 80 = 160 ÷ 2; after Z gives 40, all have 120.
Why the other options are wrong
- (a) ₹ 420
- ₹420 does not satisfy both conditions; the only solution is X = 80, Y = 120, Z = 160.
- (c) ₹ 300
- ₹300 does not satisfy both conditions; the total is ₹360.
- (d) ₹ 270
- ₹270 does not satisfy both conditions; the total is ₹360.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.