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?
- (a) 6 hours 15 minutes
- (b) 6 hours 30 minutes
- (c) 6 hours 45 minutes ✓ UPSC's answer
- (d) 7 hours
Why the answer is (c)
• Hourly work: X does 1/6, Y does 1/8 and Z does 1/8 of the job. To finish fastest, the fastest worker X should work as often as the rule allows — every alternate hour.
• Schedule X, Y, X, Z, X, Y for the first 6 hours: X works 3 hours (3/6 = 1/2) and Y and Z together 3 hours (3/8). Work done = 1/2 + 3/8 = 7/8.
• 1/8 of the job remains. Hour 7 can go to X again (Y worked in hour 6), and X needs (1/8) ÷ (1/6) = 3/4 hour = 45 minutes.
• X cannot work more than 3 of the first 6 hours, so no schedule is faster. Minimum time = 6 hours 45 minutes, option (c).
Why the other options are wrong
- (a) 6 hours 15 minutes
- 6 hours 15 minutes is incorrect because the remaining work after 6 hours (1/8) takes 45 minutes for X to complete, not 15 minutes.
- (b) 6 hours 30 minutes
- 6 hours 30 minutes is incorrect because the remaining work (1/8) requires 45 minutes of work by the fastest available worker (X), not 30 minutes.
- (d) 7 hours
- 7 hours is incorrect because the work is completed in 6 hours and 45 minutes, which is less than 7 hours.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.