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Question

A can do a piece of work in $$14$$ days and B in $$21$$ days. They begin together, but $$3$$ days before the completion of the work, A leaves off. In how many days is the work complete?


A
10 days
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B
1015days
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C
15 days
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D
7 days
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Solution

The correct option is B $$10\dfrac {1}{5} days$$
$$(A + B)'s 1$$ day work
$$= \dfrac {1}{14} + \dfrac {1}{21} = \dfrac {3 + 2}{42} = \dfrac {5}{42}$$
At the end, B works for $$3$$ days so work done by B in $$3\ days = 3\times \dfrac {1}{21} = \dfrac {1}{7}$$.
Remaining work $$1 - \dfrac {1}{7} = \dfrac {6}{7}$$ which is to be done by A and B.
$$\dfrac {5}{42}$$ of work $$(A + B)$$ can do in $$1$$ days
$$\therefore \dfrac {6}{7}$$ of work $$(A + B)$$ can do in $$\dfrac {1}{5/42} \times \dfrac {6}{7} = 7 \dfrac {1}{5}days$$
$$\therefore$$ Time to complete the work
$$= 3 + 7 \dfrac {1}{5} = 10\dfrac {1}{5}days$$.

Mathematics

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