Question

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?

Answer 1

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: \(\frac{1}{20}\)

Work done by B in one hour: \(\frac{1}{24}\)

Work done by C in one hour: \(\frac{1}{x}\)

Work done by A, B and C together in a one hour : \(\frac{1}{8}\)

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

⇒ 88X +960 = 120X

⇒ 32X = 960

⇒ X = \(\frac{960}{32}\) = 30 hours

∴ C can do the work 30 hours.