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A can do a piece of work in 25 days. While B alone can do in 20 days. A started the work and was Joined by B after 10 days. The work lasted for

A. \(12\frac{1}{2}\) days

B. 15 days

C. \(6\frac{1}{2}\)

D. 25 hours

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Number of hours A required do a piece of work : 25 

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

Work done by A in one hour: \(\frac{1}{25}\)

Work done by B in one hour: \(\frac{1}{20}\)

A works alone for 10 hours, so work completed by A in 10 hours : \(10\times\frac{1}{25}=\frac{2}{5}\)

Work left = \(1-\frac{2}{5}=\frac{3}{5}\)

Work done by A and B together in one hour: \(\frac{1}{25}+\frac{1}{20}=\frac{9}{100}\)

They can do the work together in \(\frac{100}{9}\) hours.

But \(\frac{3}{5}\)th of the work is done by both A and B

∴ Time required to complete \(\frac{3}{5}\)th of the work together by A and B : \(\frac{3}{5}\times\frac{100}{9}=\frac{20}{3}\)hours

∴ Time taken to finish the work: \(\frac{20}{3}=\frac{2}{3}\)hours

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