Explanation:

- Calculate the filling rates:

- First tap fills \(\frac{1}{12}\) of the tank per hour.

- Second tap fills \(\frac{1}{18}\) of the tank per hour.

- Together, they fill \(\frac{1}{12} + \frac{1}{18} = \frac{5}{36}\) of the tank per hour.

- Calculate the leakage rate:

- The leak empties \(\frac{1}{36}\) of the tank per hour.

- Combined effect in the first hour:

- \(\frac{5}{36} - \frac{1}{36} = \frac{4}{36} = \frac{1}{9}\) of the tank is filled in 1 hour.

- Remaining to fill after 1 hour:

- \(\frac{8}{9}\) of the tank left to fill.

- Rate without leakage:

- Combined rate of filling without leakage = \(\frac{5}{36}\).

- Time to fill remaining \(\frac{8}{9}\) of the tank:

- Time = \(\frac{8}{9} \div \frac{5}{36} = \frac{8}{9} \times \frac{36}{5} = \frac{32}{5} = 6.4\) hours = 6 hours 24 minutes.

- Total time = 1 hour (first hour) + 6 hours 24 minutes = 7 hours 24 minutes.

- Correct Answer: Option 3 - 7 hours 24 minutes