Pipes P and Q can fill a tank in 18 and 27 minutes, respectively, whereas pipe R can empty thefull tank in 54 minutes. P and Q were opened together for 6 minutes and then closed and R was opened. The tank was emptied by R alone in:

30 minutes

P+ = 18 min, Q+ = 27 min, R- = 54 min,

⇒ P + Q were opened for 6 min and the closed = (3 + 2) x 6 = 5 = 6 = 30 units,

⇒ R was opened, Time required by R to empty the tank = \(\frac{30}{1}\) = 30 minutes.