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

Answer 1

The correct option is B 24

Work done by $P$ per day $=\frac{W}{12}$

Let Work done by $Q$ per day $=\frac{W}{d_q}$

where $d_q$ is Number of days taken by Q to complete Work Alone

$P$ and $Q$ can together do the Work per day $=\frac{W}{8}$

Now, using the Given Information

$\Rightarrow \frac{W}{12}+\frac{W}{d_q}=\frac{W}{8}$

$\Rightarrow \frac{1}{12}+\frac{1}{d_q}=\frac{1}{8}$

Solving Further we get

$\Rightarrow d_q=24$

Therefore Answer is $\left(B\right)$