Pipes M and N can empty the tank in 21 minutes and 28 minutes respectively. They are opened alternately for one minute each, starting with N. The time taken to empty the tank is
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So when all 3 pipes work together, total inflow of water into the cistern per minute is 2+(8/9)+(1/2)=61/18 liters. Time needed to fill 122 liters = 122/(61/18) = (122*18)/61 = 2*18 = 36 minutes.
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