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A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the work.

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Number of days A required do a piece of work : 16 

Number of days B required do a piece of work : 12

Work done by A in one day: \(\frac{1}{16}\)

Work done by B in one day: \(\frac{1}{12}\)

A works alone for 2 days, so work completed by A in 2 days : \(2\times\frac{1}{16}=\frac{1}{8}\)

Work left = \(1-\frac{1}{8}=\frac{7}{8}\)

Work done by A and B together in one day: \(\frac{1}{16}+\frac{1}{12}=\frac{7}{48}\)

They can do the work together in \(\frac{48}{7}\) days.

But \(\frac{7}{8}\)th of the work is done by both A and B

∴ Time required to complete \(\frac{7}{8}\)th of the work together by A and B : \(\frac{7}{8}\times\frac{48}{7}\) = 6 days

∴ Time taken to finish the work 6 + 2 = 8 days ( here 2 is added because\(\frac{1}{8}\)work is done by A alone).

∴ Total time taken to finish the work: 8 days

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