A, B, and C can complete a work in 24, 36, and 72 days respectively. A works daily, and B and C assist him every 4th day. In how many days will the work be completed?
Show answer & explanation
Correct answer: B
Explanation
A's work in 1 day = 1/24
B's work in 1 day = 1/36
C's work in 1 day = 1/72
For the first 3 days, only A will work -
A's work in 3 days = 3 × 1/24 = 3/24 = 1/8
On the fourth day, A, B, and C will all work together -
A + B + C = 1/24 + 1/36 + 1/72
= 3/72 + 2/72 + 1/72
= 6/72 = 1/12
Total work in 4 days = 1/8 + 1/12
= 3/24 + 2/24 = 5/24
Work done in 16 days (i.e., 4 cycles) -
4 × 5/24 = 20/24 = 5/6
Remaining work = 1 - 5/6 = 1/6
On the 17th, 18th, and 19th days, only A will work -
A's work in 3 days = 3/24 = 1/8
Remaining work -
1/6 - 1/8
= 4/24 - 3/24 = 1/24
On the 20th day, A, B, and C will work together again -
Work in 1 day = 1/12
Time taken to complete 1/24 of the work:
(1/24) ÷ (1/12) = 1/2 day
Total time = 19 + 1/2 = 19.5 days