A, B and C can do a piece of work in 22 days, 24 days and 33 days, respectively. In how many days will the work be finished if, A works on the 1st day, C works on the 2nd day, B works on the 3rd day, A works on the 4th day and so on?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 25 .
Work done per day,
A = 1/22, B = 1/24, C = 1/33
3-day cycle work: A + C + B = 1/22 + 1/33 + 1/24
A = 12/264, B = 11/264, C = 8/264 (LCM of 22, 33, 24 = 264)
Work in 3 days = 12 + 8 + 11 = 31/264
Number of full 3-day cycles = 8 → Work done = 8 × 31/264 = 248/264
Remaining work = 1 − 248/264 = 16/264 = 2/33
Next day A works → A’s 1 day work = 12/264 = 1/22
Fraction of day needed = (2/33) ÷ (1/22) = 44/33 = 4/3 days
Total time = 8 × 3 + 4/3 = 24 + 4/3 = 25 1/3 days