Question

P alone can complete a work in 12 days while P and Q together can complete the same work in 8 days. Find the number of days that Q will take to complete the work alone?

A
10
B
24
C
20
D
9

Solution

The correct option is B 24Work done by $$P$$ per day $$=\dfrac{W}{12}$$Let Work done by $$Q$$ per day $$=\dfrac{W}{d_q}$$where $$d_q$$ is Number of days taken by Q to complete Work Alone$$P$$ and $$Q$$ can together do the Work per day $$=\dfrac{W}{8}$$ Now, using the Given Information$$\Rightarrow \dfrac{W}{12}+\dfrac{W}{d_q}=\dfrac{W}{8}$$$$\Rightarrow \dfrac{1}{12}+\dfrac{1}{d_q}=\dfrac{1}{8}$$Solving Further we get$$\Rightarrow d_q=24$$Therefore Answer is $$(B)$$ Mathematics

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