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A and B can do a piece of work in 20 days and 12 days respectively. A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work last ? 

(a) 10 days 

(b) 20 days 

(c) 15 days 

(d) 6 days

1 Answer

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(a) 10 days

A’s one days’ work = \(\frac{1}{20}\)

B’s one days’ work = \(\frac{1}{12}\)

Work done by A in 4 days = \(\frac{4}{20}\) = \(\frac{1}{5}\)

Remaining work = 1 - \(\frac{1}{5}\) = \(\frac{4}{5}\)

(A + B)’s 1days’ work = \(\frac{1}{20}\) + \(\frac{1}{12}\) = \(\frac{2}{15}\)

\(\therefore\) Number of days to do the remaining work = \(\frac{4}{5}\div\frac{2}{15}\) = \(\frac{4}{5}\times\frac{15}{2}\) = 6 days

\(\therefore\) Total number of days taken in the completion of work = 6 + 4 = 10 days

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