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
B
11
C
13
D
15

Solution

## The correct option is C 13Work 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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