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Question

A is twice as good a workman as B and together they can finish a piece of work in $$12$$ days. In how many days A alone can finish the work?


A
18
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B
27
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C
36
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D
None of these
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Solution

The correct option is B $$18$$
Given:
$$A$$ is twice as good a workman as $$B$$ and together they can finish a piece of work in $$12$$ days
Let the work done by $$B$$ be $$X$$.
$$\therefore$$ Work done by $$A=2x$$
Work done by $$A$$ and $$B$$ together in $$12$$ days $$=1$$
Work done by $$A$$ and $$B$$ together in $$12$$ days $$=\dfrac{1}{12}$$

$$\Rightarrow $$ Work done by $$A$$ in $$1$$ days + Work done by $$B$$ in $$1$$ day $$=\dfrac{1}{12}$$

$$\Rightarrow x+2x=\dfrac{1}{12}$$

$$\Rightarrow 3x=\dfrac{1}{12}$$

$$\Rightarrow x=\dfrac{1}{36}$$

$$\therefore$$ Work done by $$A$$ in $$1$$ day $$=2x=2\times \dfrac{1}{36}=\dfrac{1}{18}$$

Hence, $$A$$ to finish the work alone required $$18$$ dyas

$$\therefore$$ Option $$A$$ is correct.

Mathematics

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