Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone ?
- (a) 6 days
- (b) 8 days
- (c) 10 days ✓ UPSC's answer
- (d) 11 days
Why the answer is (c)
• Let the total work be 100 units. Ram and Shyam together complete 60 units in 4 days, so their combined rate is 15 units/day.
• Shyam completes the remaining 40 units in 8 days, so Shyam's individual rate is 5 units/day.
• Ram's individual rate is the combined rate minus Shyam's rate: 15 - 5 = 10 units/day.
• To complete the entire 100 units alone, Ram would take 100 / 10 = 10 days.
• Therefore, the correct option is (c).
Why the other options are wrong
- (a) 6 days
- 6 days is incorrect because it does not account for the difference in individual work rates derived from the given time periods.
- (b) 8 days
- 8 days is incorrect because it assumes Ram works at the same rate as Shyam, ignoring that Ram is faster.
- (d) 11 days
- 11 days is incorrect because the calculation of Ram's rate (10 units/day) leads to exactly 10 days, not 11.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.