X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
Answer & explanation
Answer: (c) 6 hours 45 minutes
X is the fastest, so X should take the first hour and every alternate hour after it. In six hours 21 of the 24 units are done, and X finishes the last 3 units in 45 minutes of the seventh hour.
- Take the work as 24 units (LCM of 6 and 8): X does 4 units per hour, Y 3 and Z 3.
- Nobody may work two hours in a row, so X can work at most every other hour; start with X so that he gets as many hours as possible.
- Hours 1 to 6: X, Y, X, Z, X, Y gives 3 × 4 + 3 × 3 = 21 units, and all three have worked.
- Hour 7 is X’s again: the remaining 3 units at 4 units per hour take 3/4 hour = 45 minutes.
- Total = 6 hours 45 minutes.
- Check: if Y or Z starts, X still gets only three of the first six hours (21 units), but hour 7 then goes to Y or Z at 3 units per hour, finishing at exactly 7 hours.
Remember · In alternate-hour work problems, give the fastest worker the first slot and every second slot after it.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·