  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  B
27  C
36  D
None of these  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 $$12$$ daysLet 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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