UPSC Prelims 2021 · CSAT
Question 55: Basic Numeracy
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 ?
AnswerUPSC’s answer is (b).
Let X, Y and Z hold x, y and z rupees. If Z gives X ₹40 all three are equal: x + 40 = y = z − 40, so y = x + 40 and z = x + 80. If Y gives X ₹40, Y's remaining money is half of Z's: y − 40 = z/2, so x = (x + 80)/2, which gives x = 80. Then y = 120 and z = 160, total ₹360. Check: after Z gives 40, all have ₹120. Remember: use the equal-amounts condition first to tie all three amounts to one unknown.
Why each option is right or wrong
- (a) ₹420 gives X = 100, Y = 140, Z = 180, but then Y − 40 = 100 is not half of Z's 180.
- (b) Right: X = 80, Y = 120, Z = 160 satisfy both conditions and total ₹360.
- (c) ₹300 gives X = 60, Y = 100, Z = 140, but Y − 40 = 60 is not half of 140.
- (d) ₹270 gives X = 50, Y = 90, Z = 130, but Y − 40 = 50 is not half of 130.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.