A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
- (a) 6 ✓ UPSC's answer
- (b) 8
- (c) 10
- (d) 12
Why the answer is (a)
• Person X completes 20% of the work in 8 days, so X's daily work rate is 20/8 = 2.5% per day.
• Person Y completes 25% of the work in 6 days, so Y's daily work rate is 25/6 ≈ 4.1667% per day.
• When working together, their combined daily work rate is 2.5 + 25/6 = 15/6 + 25/6 = 40/6 = 20/3 ≈ 6.6667% per day.
• To complete 40% of the work, the time required is (40%) / (20/3 % per day) = 40 * 3/20 = 6 days.
• Therefore, the correct answer is 6 days.
Why the other options are wrong
- (b) 8
- 8 days is the time X takes to complete 20% of the work alone, not the time for both to complete 40% together.
- (c) 10
- 10 days does not correspond to the calculated combined rate of 20/3% per day for 40% of the work.
- (d) 12
- 12 days is incorrect as it significantly overestimates the time required given the combined efficiency of X and Y.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.