A tap can fill a cistern in 24 minutes and another tap can empty it in 36 minutes. If both the taps are open, the time taken to fill the tank will be:

Correct option is C

Given:
Two pipes A and B, pipe A can fill a tank in 24 minutes and pipe B can empty a tank in 36 mins
Solution:
Pipe A can fill a tank = 24 mins
A part filled by pipe A in 1 min = $$\frac{1}{24} \\$$ min​
Pipe B can empty a tank = 36 mins
A part emptied by pipe B in 1 min = $$\frac{1}{36} \\$$​​
Both pipes together can fill a tank in 1 min = $$= \frac{1}{24} - \frac{1}{36} \\$$​​

Time is taken to fill a tank both pipes together = $$= \frac{3 - 2}{72} = \frac{1}{72} \\$$ 
​$$\text{Time taken to fill the tank together} = \frac{1}{\frac{1}{72}} = 72\ \text{minutes}$$​​
Alternate Solution
Total Work = 72 units

A + B Work = 3 - 2 = 1 units
A and B can complete the whole work => 72/1 minv= 72 min
∴ The time is taken to fill a tank is 72 min.