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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
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B
24
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C
20
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D
9
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Solution

The correct option is B 24
Work 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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