Pipe A fills the tank normally in 2 hours
So, Pipe A can fill half of the tank in 1 hour
Let us consider, the leak takes x hours to empty the full tank when pipe A is shut.
So, the leak will empty $\frac{1}{\mathrm{x}}$of the tank in 1 hour.
The net amount of water that gets filled in the tank in 1 hour when pipe A and the leak are open$=\frac{1}{2}-\frac{1}{\mathrm{x}}$ of the tank---Eq 1

As per the question,
when the leak is open, time taken to fill the tank $=2\frac{1}{2}=\frac{5}{2} \mathrm{hours}$

Therefore, in 1 hour, $\frac{2}{5}$^th of the tank gets filled--Eq 2

Equating Eq1 and Eq2, we get

$$\begin{gathered} \Rightarrow \frac{1}{2}-\frac{1}{\mathrm{x}}=\frac{2}{5} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{2}-\frac{2}{5} =\frac{1}{10} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{10} \\ \Rightarrow \mathrm{x}=10 \mathrm{hours} \end{gathered}$$

Hence option D is correct.