A, B and C can do a piece of work in 20, 30 and 60 days, respectively. In how many days can A do the work if he is assisted by both B and C on every third day?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15.
A can complete the work in 20 days. So, A’s one-day work = 1/20
B can complete the work in 30 days. So, B’s one-day work = 1/30
C can complete the work in 60 days. So, C’s one-day work = 1/60
In 2 days, A works alone. So, the work done by A in 2 days = 2 × 1/20 = 2/20 = 1/10
the combined work on the 3rd day = 1/20 + 1/30 + 1/60
⇒ 3/60 + 2/60 + 1/60 = 6/60 = 1/10
In 3 days, the total work done (2 days by A alone and 1 day by A, B, and C) = 1/10 + 1/10
⇒ 2/10 = 1/5 = 5 days
Each cycle takes 3 days, so the total number of days required to complete the work is:
5 × 3 = 15 days