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Question

A is twice as good a workman as B and together they finish a price of work in $$14$$ days. In how many days can A alone finish the work?


A
13
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B
15
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C
17
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D
21
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Solution

The correct option is D $$21$$
Let the work done by B be $$x$$.
$$\therefore$$Work done by A $$= 2x$$
Work done by A and B together in $$14$$ days $$= 1$$
Work done by A and B together in $$1$$ day $$=\cfrac{1}{14}$$
$$\Rightarrow$$ Work done by A in $$1$$ day $$+$$ Work done by B in $$1$$ day $$=\cfrac{1}{14}$$
$$x + 2x = \cfrac{1}{14}$$
$$\Rightarrow \; 3x = \cfrac{1}{14}$$
$$\Rightarrow \; x = \cfrac{1}{42}$$
Work done by B in $$1$$ day $$=\cfrac{1}{42}$$
$$\therefore$$ Work done by A in $$1$$ day $$=\cfrac{1}{21}$$
Hence, to finish the work, A require $$21$$ days.
Hence, A alone can finish the work in $$21$$ days.

Mathematics

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