A and B working separately can do a piece of work in 21 and 24 days, respectively. If they work for a day alternately with A beginning the work, it would be completed in _________.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 22 days
Given,
Time is taken by A to complete the work = 21 days
so part of the work done by A in 1 day = 1/21
similarly, part of the work done by B in 1 day = 1/24
Work done by (A + B) in 2 days = (1/21+1/24) = 15/168 = 5/56 part of work
Work done by (A + B) in 11 pairs of days i.e.,
Work done by (A + B) in 22 day = (5×11)/56 = 55/56th part of work
Remaining work = 1 - 55/56 = 1/56th part of work
On the 23rd day, again A will work separately. So,
Time is taken by A to complete the 1/56th part of the work
= 1/56 × 21 days
= 3/8
Total time taken = 22 + 3/8 = 22 days