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A and B can do a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

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Best answer

Given,

 A and B can do a piece of work in = 18 days

Work done by A and B in 1 day \(=\frac{1}{18}\)

B and C can do a piece of work in = 24 days

Work done by C and B in 1 day \(=\frac{1}{24}\)

A and c can do a piece of work in = 36 days

Work done by A and C in 1 day \(=\frac{1}{26}\)

Now adding, we get,

2(A+B+C) ’s 1 day work \(=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}=\frac{4+3+2}{72}=\frac{9}{72}=\frac{1}{8}\)

A+B+C one day work \(=\frac{1}{8\times2}=\frac{1}{16}\)

∴ A, B and C can finish the work in \(=\frac{1}{\frac{1}{16}}\) =16 days

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