Two pipes can fill a tank in 20 hours and 60 hours respectively. A third pipe is an outlet pipe. If all three are opened together, the tank gets filled up in 40 hours. What time will the outlet pipe take to empty the full tank?

Correct option is D

Formula Used: Work done per hour = 1 / Time taken
Solution:
Let the rate of filling by the first pipe be 1/20 tank per hour and by the second pipe be 1/60 tank per hour.
Let the rate at which the outlet pipe empties the tank be 1/x tank per hour.
When all three pipes are opened, they together fill the tank in 40 hours.
So, the net rate of filling the tank is 1/40 tank per hour.
​$$\left( \frac{1}{20} + \frac{1}{60} - \frac{1}{x} \right) = \frac{1}{40} \\\frac{1}{20} + \frac{1}{60} - \frac{1}{40} = \frac{1}{x} \\\left( \frac{1}{15} - \frac{1}{40} \right) = \frac{1}{x} \\\Rightarrow \frac{1}{x} = \frac{1}{15} - \frac{1}{40} \\\ \\\Rightarrow \frac{1}{x} = \frac{40 - 15}{15 \times 40} = \frac{25}{600} = \frac{1}{24} \\\ \\\text{So, } x = 24$$​​