A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours and 20 minutes to fill the tank. The leak can drain all the water of the tank in:

Let the volume of the tank be 6V litres. 

If the pump takes 2 hours to fill the tank, then the capacity of the pump is $$\dfrac{6V}{2}=\ 3V\ $$litres/hour.

In 2 hours 20 minutes $$\ =\ 2\ +\ \dfrac{20}{60}\ =\ \dfrac{7}{3}$$ hours, the water produced by the pump is $$3V\ \times\ \dfrac{7}{3}\ =\ 7V$$.

We know that the tank has a volume of 6V litres. So, the leak in $$\dfrac{7}{3}\ $$hours removed 7V - 6V = V litres of water. So, in 1 hour, the leak removes $$\dfrac{3V}{7}$$ litres.

The capacity of the leak is $$\dfrac{3V}{7}$$ litres/hour. So, the time taken for the leak to empty the whole tank is 

$$6V\ \times\ \dfrac{7}{3V}\ =\ 14$$ hours.

Hence, the correct answer is option A.