A can do a piece of work in 80 days. He works on it for 10 days and then, B alone finishes the remaining work in 49 days. In how much time will A and B, working together, finish the work?

Work done by A in 10 days = 10/80 = 1/8 Remaining work = (1-(1/8)) = 7/8 Now, work will be done by B in 49 days. Whole work will be done by B in (49 * 8/7) = 56 days Therefore, A's one day's work = 1/80 B’s one day's work = 1/56(A + B)'s one day's work = 1/80 + 1/56 = 17/560 = 33 days Hence, both will finish the work in 33 days.