Working alone, A can do a piece of work in 20 days and B can do the same work in 30 days. They work together and A leaves 5 days before the work is completed and B completes the work. How long did it take for the entire work to be completed?

Explanation:

A and B working together will complete 1\20+1\30=5\60

= 1\12th of the work in a day.

Let the work be completed in ‘x’ days from the start.

Therefore, A and B worked together for (x-5) days and B alone worked for another 5 days to complete the entire work

Therefore, x−5\12+5\30=1

Solving for x, we get 5(x-5) + 10 = 60 or 5x = 75 or x = 15 days.