Let the volume of tank be 1 unit.
We have, rate of filling the tank without a leak = 1 unit per 2 hours.
And the rate of filling in the presence of a leak = 1 unit per 2 hours 20 minutes = 1 unit per 7/3 hours.
Now, the rate of emptying the tank = 1/2 - 1/(7/3) =1 unit per 14 hours.
Then, time taken to empty the tank = 14 hours