According to the question,

part of the tank filled by pump in 1 hour=$\frac{1}{2}$

Because of the leak, part of the tank emptied by pump in 1 hour=$\frac{1}{{\displaystyle 2\frac{1}{3}}}=\frac{1}{{\displaystyle \frac{7}{3}}}=\frac{3}{7}$

part of the tank emptied by the leak in 1 hour$=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14}$

The tank will be emptied in 14 hours.

Hence option D is correct.