# A can do a piece of work in 20 days while B alone can do In 12 days. B worked at it for 9 days. A can finish the remaining work in

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A can do a piece of work in 20 days while B alone can do In 12 days. B worked at it for 9 days. A can finish the remaining work in

A. 3 days

B. 5 days

C. 7 days

D. 11 days

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Number of days A required do a piece of work : 20

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

Work done by A in one day: $\frac{1}{20}$

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

B works alone for 9 days, so work completed by B in 9 days : $9\times\frac{1}{12}=\frac{3}{4}$

Work left = $1-\frac{3}{4}=\frac{1}{4}$

But $\frac{3}{4}$th of the work is already done by B

∴ Time required to complete the remaining $\frac{1}{4}$th of the work by A : $\frac{1}{4}\times20$ = 5 days

∴ Time taken to finish the work 9 + 5 = 14 days

∴ A can finish the remaining work in : 5 days