Two taps can fill a tank in 20 minutes and 30 minutes respectively. There is an outlet tap at exactly half level of that rectangular tank which can pump out 50 litres of water per minute. If the outlet tap is open, then it takes 24 minutes to fill an empty tank. What is the volume of the tank?

Let the volume of the tank be v litres.

Pipe 1 : 1 min = v/20 lt fill 

Pipe 2 : 1 min = v/30 lt fill

Pipe 3: 1 min = v/50 lt empty

Both inlet pipes can together fill the tank in 20*30/20+30 = 600/50 = 12 minutes, half a tank in  6 minutes.

So, for 6 minutes, both inlet pipe work and for (24-6) = 18 minutes both inlet and one outlet pipes work.

1/2 {6v/20 + 6v/30} +1/2{ 18v/20 + 18v/30 -18v/ 50} = v

v = 1800 litres