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

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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?

posted Jun 7, 2016

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

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.

answer Jun 10, 2016 by anonymous

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