Question

A can do a piece of work in 25 days which B alone can do in 20 days. A started the work and joined B after 10 days. the work lasted for

Answer 1

Work done by A in l0 days = (1/25) *10 = 2/5
Remaining work = 1 - (2/5) = 3/5 
(A+B)s 1 days work = (1/25) + (1/20) = 9/100
9/100 work is done by them in 1 day. 
hence 3/5 work will be done by them in (3/5)*(100/9)
= 20/3days. 
Total time taken =  (10 + 20/3) = 16*(2/3) days