Two taps A and B can fill a tank in 8 hrs. and 12 hrs. respectively. Both pipes are opened together, but due to a leak in the bottom it takes 12 minutes more to fill the tank. Find the time taken to the leak to empty the full tank.

Per hour A and B together fills  $\frac{1}{8}+\frac{1}{12}=\frac{5}{24}$ part of the tank

time taken by A and B to fill the tank=$\frac{24}{5}hrs$

due to leakage it takes 12 minutes more to fill the tank i.e $\frac{24}{5}+\frac{12}{60}=\frac{300}{60}=5 hrs$

let the time taken to empty the tank is x hrs

when all the three pipes opened together per hr they can fill

$\frac{1}{8}+\frac{1}{12}-\frac{1}{x}=\frac{1}{5}$

$\frac{1}{x}=\frac{1}{8}+\frac{1}{12}-\frac{1}{5}=\frac{15+10-24}{120}=\frac{1}{120}$

the leakage pipe empty the tank in 120 hrs