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?
Answer & explanation
Answer: (b) ₹ 360
The second condition gives X + 40 = Y = Z − 40, and the first gives Y − 40 = Z/2. Solving, Z = 160, Y = 120 and X = 80, a total of ₹360.
- Let X, Y and Z have x, y and z rupees.
- If Z gives X ₹40, all three are equal: x + 40 = y = z − 40.
- If Y gives X ₹40, Y has half of Z: y − 40 = z/2.
- Put y = z − 40: z − 80 = z/2, so z = 160, y = 120, x = 80.
- Total = 80 + 120 + 160 = ₹360.
- Check: after Y gives ₹40, Y has 80, half of Z's 160; after Z gives ₹40, everyone has 120.
Remember · Turn 'then all will be equal' into a chain of equalities; it reduces everything to one unknown.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·