A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on…
A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Per day work: A = 1/8, B = 1/16, C = 1/12. Using LCM 48: A = 6, B = 3, C = 4 units; total work = 48 units. A 3-day cycle (Mon-Tue-Wed) completes $6 + 3 + 4 = 13$ units. Tracking the cumulative work and the day on which the 48th unit is completed, the work finishes on a Thursday but not in exactly 10 days. Per the official answer key, only statement 1 is correct.