P can do a piece of work in 30 days and Q in 40 days. They work together for 4 days and then Q leaves. The number of days taken by P to finish the remaining work is:

To find the number of days taken by P to finish the remaining work, we can break down the work done by both P and Q step-by-step.

Let the total work be represented as 1 unit.

P can complete the work in 30 days. Therefore, the work done by P in 1 day is:
$\frac{1}{30}$
Similarly, Q can complete the work in 40 days. Therefore, the work done by Q in 1 day is:
$\frac{1}{40}$

When P and Q work together, their combined 1-day work is:
$\frac{1}{30}+\frac{1}{40}$
To add these fractions, we find the least common multiple (LCM) of 30 and 40, which is 120:
$\frac{4+3}{120}=\frac{7}{120}$

They work together for 4 days, so the total work completed by both in 4 days is:
$4\times \frac{7}{120}=\frac{7}{30}$

The remaining work after Q leaves is:
$1-\frac{7}{30}=\frac{23}{30}$

Now, P has to finish this remaining work of $\frac{23}{30}$ alone. Since P's 1-day work rate is $\frac{1}{30}$, the time taken by P to finish the remaining work is:
$\text{Number of days}=\frac{\text{Remaining Work}}{\text{P's 1-day work}}=\frac{\frac{23}{30}}{\frac{1}{30}}=23\text{days}$

Thus, P takes 23 days to finish the remaining work.

The correct option is 23 days.