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Question

$$P$$ is $$30\%$$ more efficient than $$Q. P$$ can complete a work in $$23$$ days. If $$P$$ and $$Q$$ work together, how much time will it take to complete the same work?


A
9
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B
11
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C
13
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D
15
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Solution

The correct option is C 13
Work done by $$P$$ in $$1$$ day$$=\dfrac{1}{23}$$
Let work done by $$Q$$ in $$1$$ day$$=q$$
$$q\times\dfrac{130}{100}=\dfrac{1}{23}$$
$$\Rightarrow\,q=\dfrac{100}{23\times 130}=\dfrac{10}{23\times 13}$$
Work done by $$P$$ and $$Q$$ in $$1$$ day$$=\dfrac{1}{23}+\dfrac{10}{23\times 13}=\dfrac{23}{23\times 13}=\dfrac{1}{13}$$
$$\therefore\,P$$ and $$Q$$ together can do the work in $$13$$ days.


Mathematics

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