X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in 8 2/3 days. What is n equal to?
Answer & explanation
Answer: (b) 4
Alone, X, Y and Z would take 18, 24 and 16 days, i.e. 8, 6 and 9 units a day out of 144 units. Y's last 8 2/3 days cover 52 units, leaving 92 units done together at 23 units a day, so n = 4.
- Full-work times: X = 6 × 3 = 18 days, Y = 8 × 3 = 24 days, Z = 12 × 4/3 = 16 days.
- Take the work as 144 units (LCM of 18, 24, 16). Daily work: X = 8, Y = 6, Z = 9 units; together 23 units a day.
- Y alone for 8 2/3 = 26/3 days does 6 × 26/3 = 52 units.
- Work done by all three together = 144 − 52 = 92 units, so n = 92 ÷ 23 = 4 days.
- Check: 4 × 23 + 52 = 92 + 52 = 144.
Remember · Turn partial-work data into full-work days, take the LCM as total units, then work in units per day.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·