Pipes A and B can fill a tank in 18 minutes and $$22\frac{1}{2}$$ minutes, respectively while pipe C can empty the full tank in 12 minutes. A and are opened together for 6 minutes and then closed. Now C is opened. C alone will empty the tank in ..........

Time taken by Pipe A to completely filled the tank = 18 min

Time taken by Pipe B to completely filled the tank = $$22\frac{1}{2} = \frac{45}{2}$$

Time taken by Pipe C to empty the tank = 12 min

Let the total capacity of tank be 180 units.

(LCM of 18, 45/2 and 12 is 180)

Efficiency of pipe A = 180/18 = 10

Efficiency of pipe B = 180 $$\times \frac{2}{45}$$ = 8

 Efficiency of pipe C = -180/12 = -15

work done by pipe A and B in 6 min = 6 $$\times (10 + 8)$$ = 108

Time taken by pipe C to empty 108 units = 108/15 = $$7\frac{1}{5}$$ min