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Question

A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B can do the work in _______.


A
12 days
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B
15 days
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C
20 days
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D
30 days
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Solution

The correct option is D $$15$$ days
Given, Work Efficiency ratio of A:B is 3:1
Let B takes $$x days$$ to do the work. So according to the question, A takes $$x-10\: days$$ to do the same work. Time ratio and efficiency ratio are inversely proportional. So equating the ratios,
$$\dfrac{x-10}{x}=\dfrac{1}{3}$$
$$\implies x=15$$
Therefore, B can finish the work alone in $$15\: days$$

Mathematics

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