Question

A, B and C working together can do 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

Given,

 A can do a piece of work in 20 hours 

Work done by A in 1 hour \(=\frac{1}{20}\)

B can do same work in = 24 hours

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

A,B and C working together can do that work in = 8 hours

Work done by A, B, C together in 1 hour \(=\frac{1}{8}\)

∵ work done by C in 1 hour = (work done by A,B,C in 1 hour) – ( work done by A And B in 1 hr) \(=\frac{1}{8}-[\frac{1}{20}+\frac{1}{24}]=\frac{1}{8}-\frac{11}{120}=\frac{15-11}{120}=\frac{4}{120}=\frac{1}{36}\)

∴ Time taken by C to complete the work \(=\frac{1}{\frac{1}{20}}\) = hours