Two taps A and B can fill an empty tank in 8 hours and 12 hours respectively. But due to leak at the bottomthe two taps together took 1 hour 12 min moretimeto fill the tank. Then the time. in hours, in which the leak alone can empty a full tank of water is

As per the question,

A can empty tank in 8 hour and B can empty the tank in 12 hour.

If A and B both open at a time, then tank will be fill in one hour$$\dfrac{1}{8}+\dfrac{1}{12}=\dfrac{3+2}{24}=\dfrac{5}{24}$$

Hence tank will be filled, together by A and B $$\dfrac{24}{5}hour$$

Let C can empty the tank in in x hour.

Hence, it will be filled $$\dfrac{5}{24}-\dfrac{1}{x}=\dfrac{1}{6}$$

$$\dfrac{1}{x}=\dfrac{5-4}{24}=\dfrac{1}{24}$$

Hence, leak can empty the tank in 24 hour.