Pipes X and Y can independently fill a tank in 80 minutes and 90 minutes respectively, while pipes X and Z together take 3 hours to fill the same tank. If pipes X and Y are turned on for the first 36 minutes, after which pipe X is turned off and pipe Z is turned on, how long will it take in total to fill the tank?

Solution

ATQ, Let total capacity of the tank = 720 litres Quantity of water filled by pipe X in one minute = 720/80 = 9 litres Quantity of water filled by pipe Y in one minute = 720/90 = 8 litres Quantity of water filled by pipes X and Z together in one minute = 720/180 = 4 litres Quantity of water emptied by pipe Z in one minute = 9 – 4 = 5 litres Quantity of water filled by pipes X and Y together in 36 minutes = 36 × 17 = 612 litres Time taken to fill the remaining tank = (720 – 612)/(8 – 5) = 36 minutes Desired time = 36 + 36 = 72 minutes