A can do a job in 20 days, B in 30 days. They work on alternate days, with A starting the job. In how many days is the job finished?
Show answer & explanation
Correct answer: C
Explanation
Given:
A = 20 days, B = 30 days; working on alternate days, with A starting first.
A's rate = 1/20, B's rate = 1/30.
Work done in 2 days = 1/20 + 1/30 = 1/12.
Work done in 10 days (5 cycles) = 5/12.
Work done in 12 days (6 cycles) = 6/12 = 1/2.
On the 13th day (A) ⇒ Total work = 1/2 + 1/20 = 11/20.
Remaining work = 9/20.
On the 14th day (B) ⇒ Work done = 1/30.
Total work = 11/20 + 1/30 = 7/12.
Remaining work = 5/12.
Now, A and B will continue working in the same manner.
Every 2 days = 1/12.
After reaching 7/12, 5 more cycles (10 days) ⇒ +5/12 = 12/12 = 1 (Complete work).
Total days = 14 + 10 = 24 days.