Pipe A can fill a cistern in 4 hours while pipe B can empty it in 6 hours. How many hours would be taken...

Question

Pipe A can fill a cistern in 4 hours while pipe B can empty it in 6 hours. If both of them are opened together at the same time when the tank is empty, then how many hours would be taken by them to fill it?

Answer 1

12 hours
Pipe A can fill the cistern in 4 hours
Therefore in 1 hour pipe A can fill 1/4 of the cistern
Pipe B can empty the cistern in 6 hours
Therefore in 1 hour pipe B can empty 1/6 of the cistern

Therefore together in 1 hour they can fill 1/4 - 1/6 of the cistern
Taking LCM, (6 - 4)/24 i.e. 2/24 can be filled in 1 hour
That is 1/12 of the cistern can be filled in 1 hour
To fill the one cistern, we will need 12 hours

Answer 2

The answer is 12 hours.
In 12 hours the tank is filled up 3 times and the tank is emptied two times, therefore after twelve hours the tank will be filled up.