Explanation:

- Pipe A can fill the tank in 12 hours. Therefore, Pipe A fills \(\frac{1}{12}\) of the tank per hour.

- Pipe B can fill the tank in 8 hours. Thus, Pipe B fills \(\frac{1}{8}\) of the tank per hour.

- Pipe C can empty the tank in 15 hours, meaning Pipe C empties \(\frac{1}{15}\) of the tank per hour.

- When all pipes are opened:

- Combined filling rate = \(\frac{1}{12} + \frac{1}{8} - \frac{1}{15}\)

- Calculating the above:

- \(\frac{1}{12} = \frac{5}{60}\)

- \(\frac{1}{8} = \frac{7.5}{60}\)

- \(\frac{1}{15} = \frac{4}{60}\)

- Total = \(\frac{5}{60} + \frac{7.5}{60} - \frac{4}{60} = \frac{8.5}{60} = \frac{17}{120}\)

- If all pipes run together for 5 hours, \(\frac{17}{120} \times 5 = \frac{85}{120} = \frac{17}{24}\).

- Correct Option:

- Option: 1, 17/24