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Choose the correct option.

A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days to complete the work is:

A6 3/5

B8 1/2

C10 1/5

D13 1/2

Answer: Option C


A's 1 day work = \(\frac{1}{14}\)
B' 1 day work = \(\frac{1}{21}\)

A left 3 day before the completion of work.
B's 3 days' work = \(\frac{1}{21} \times 3 = \frac{1}{7}\)
Remaining work = \(1 \times \frac{1}{7} = \frac{6}{7}\)

(A + B)'s 1 day's work = \(\left(\frac{1}{14} + \frac{1}{21}\right) = \frac{5}{42}\)

Now, \(\frac{5}{42}\) work is done by A and B = 1 day.
whole work done by A&B = \(\frac{42}{5}\)
\(\frac{6}{7}\) part of work done by A and B = \(\frac{42}{5} \times \frac{6}{7} = \frac{36}{5}\) days.

Hence, total time taken = (3+36/5)days = \(10\frac{1}{5}\) days.

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