A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

Number of hours A required do a piece of work : 20 hours

Number of hours B required do a piece of work : 24 hours

Let number of hours C required to do a piece of work : X hours

Number of hours required by A, B and C together to do a piece of work : 8 hours

Work done by A in one hour:

Work done by B in one hour:

Work done by C in one hour:

Work done by A, B and C together in a one hour :

Work done by A, B and C together in one hour : = = =

=

⇒ 88X +960 = 120X

⇒ 32X = 960

⇒ X = = 30 hours

C can do the work 30 hours.