Pipe P can fill a tank in 25 hours and Pipe Q can emptied it is 30 hours. Pipe P starts filling and they opened for 1 hour each alternatively in what time will the tank be full?

Solution

Let the tank capacity be 150 litres  (LCM of 25 and 30) So, Pipe P can fill it in 25 hours therefore, Pipe P can fill per hours = 150/25 = 6 litres Pipe Q can emptied it in 30 hours = 150/30 = 5 litres Tank filled after 2 hours = 6 - 5 = 1 litres  (If pipes open alternatively) In last hour pipe P fill tank 6 litres So rest part of tank needed to be filled is = 150 - 6 = 144 litres In 2 hours tank filled = 1 litres So, 144 litres to be filled in = 144 × 2 = 288 therefore, So total time = 288 + 1 = 289 hours