P and Q are filling pipes which can fill a tank in 15 minutes and 20 minutes respectively. R is an empting pipe which can empty the full tank in 30 minutes. The three pipes are operated continuously one after the other in the order of P,Q and R , each being kept opened for 2 minutes until the tank is filled . After how much time will the tank be full . how to solve this question using ratio method.

32minute 40 second

Time taken by P alone to fill tank = 15 mins
Time taken by Q alone to fill the tank = 20 mins
Time taken by R alone to empty tank = 30 mins

Let the capacity of the tank be 60x [60 = LCM of 10, 20 and 30]
Rate of flow of pipe = Capacity of tank/Time taken by pipe to fill or empty tank
=> Rate of flow of P = 60x/15 = 4x
=> Rate of flow of Q = 60x/20 = 3x
=> Rate of flow of R = 60x/30 = 2x

Total water filled into the tank by ONE sequence of pipes opening = (4x*2) + (3x*2) - (2x*2) = 2x units of water in (2 + 2 + 2) = 6 mins. Hence, it would take 30 such 6 minute cycles to fill 60x units of water.
=> Time taken to fill up the tank = 30*6 = 180 mins.