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:

Given:

Tap 1 fills the cistern in 24 minutes.

Tap 2 empties the cistern in 36 minutes.

Formula used:

Net rate of filling = Rate of filling by Tap 1 - Rate of emptying by Tap 2

Time taken = Volume / Net rate of filling

Calculations:

Rate of filling by Tap 1 = 1/24 cistern/min

Rate of emptying by Tap 2 = 1/36 cistern/min

Net rate of filling = 1/24 - 1/36

⇒ Net rate = (3 - 2) / 72 = 1/72 cistern/min

Time taken to fill the cistern = 1 / (1/72) = 72 minutes

∴ The correct answer is option (1).