Tap A can fill a tank in 20 hours and tap B can empty it is 25 hours. Tap A starts filling and they opened for 1 hour each alternatively in what time will the tank be full?

Solution

Let tank capacity is = 100 ltr LCM of 20 and 25 So tap A can fill it in 20 hours ∴ Tap A can fill per hours = 100/20 = 5 ltr Tap B can empty it in 25 hours ∴ Tap B can empty per hours = 100/25 = 4 ltr Tank filled after 2 hour = 5 - 4 = 1 ltr (If taps open alternatively) In last hour tap A fill tank 5 ltr  So rest part of tank need to be filled is = 100 - 5 = 95 ltr In 2 hours tank filled = 1 ltr So 95 ltr to be filled in = 95 × 2 = 190 ∴ So total time = 190 + 1 = 191 hours