A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?

Detailed Solution:

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 42 days. Whole work will be done by B in (42*8/7)=48 days Therefore, A's one day's work=1/80 B’s one day's work=1/48 (A+B)'s one day's work=1/80+1/48=8/240=1/30 Hence, both will finish the work in 30 days.