Question

A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work?

Answer 1

According to the question, 
A can do the work in 20 days
Thus work done by A in 1 day = 1/20
Similarly, work done by B in 1 day = 1/30

So, when both A and B work together, work done
= 1/20 + 1/30
= 5/60 = 1/12
Work done by A and B in 7 days = 7 x 1/12 = 7/12
Work left to done = 1 - 7/12 = 5/12

According to question, C does 5/12 of the work in 10 days
Thus work done by C in 1 day = 5/12 x 1/10 = 1/24
As C does 1/24 of the work in 1 day, he does the whole of the work in 24 days

Hope that helps !!