Explanation:

- Pipe P fills the tank in 18 minutes. It fills 1/18 of the tank per minute.

- Pipe Q fills the tank in 27 minutes. It fills 1/27 of the tank per minute.

- Combined, P and Q fill the tank in (1/18 + 1/27) = 1/10.8 of the tank per minute.

- In 6 minutes, P and Q together fill 6 * (1/10.8) = 5/9 of the tank.

- Pipe R empties the tank in 54 minutes, or 1/54 of the tank per minute.

- When R is opened, 5/9 of the tank remains.

- To empty 5/9 of the tank, R takes (5/9) / (1/54) = 30 minutes.

- Option:1, 30 minutes is the correct answer.