A, B, and C can complete a job in 24, 36, and 72 days, respectively. A works every day, while B and C join A every fourth day. How long will it take to finish the task?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 19.5 days.
Let total work = LCM of 24, 36, and 72 = 72
A's 1 day work = 72/24 = 3
B's 1 day work = 72/36 = 2
C's 1 day work = 72/72 = 1
Work done in 3 days by A = 3 × 3 = 9
Work done on 4th day (A, B, and C together) = 3 + 2 + 1 = 6
Total work done in 4 days = 9 + 6 = 15
Total work done in 5 cycles (5 × 4 = 20 days) = × 4 = 60
Remaining work = 72 - 60 = 12
Work done by A on 17th to 19th day = 3 + 3 + 3 = 9
Remaining work = 12 - 9 = 3
Time required by A, B, and C together = 3/6 = 1/2 days
Total time = 19 + 1/2 = 19.5 days