A cistern or a water tank is always connected with two types of pipes .One which fills it up and the other which empties it out. The pipe which fills up the cistern is called an inlet and the one which empties it is called an outlet.
Let an inlet fill up a cistern in 8 hours. Then-in one hour it fills up 1/8 th part of it. We can also say that the work done by inlet in 1 hour is 1/8 , Similarly, if an outlet empties out a cistern in 6 hours, then in one hour it empties out 1/6 th part of the cistern i.e. the work done by the outlet in one hour is 1/6.
The work done by the inlet is always positive whereas the work done by the outlet is always negative.
We shall now discuss some problems on pipes and cisterns.
In one hour the tap fills 1/6 th part of the cistern
In one hour the pipe empties 1/8 th part of the cistern.
Thus, in one hour = 1/24th part of the cistern is failed.
Hence, the cistern is filled in 24 hours.
Example : A pipe can fill a cistern in 6 hours. Due to a leak in the bottom it is filled in 7 hours. When the cistern is full, in how much time will it be emptied by the leak?
Solution :
When there is no leakage, the pipe can fill the cistern in 6 hours.
The pipe fills 1/6 th part of the cistern in one hour.
When there is leakage, the pipe can fill the cistern in 7 hours. Thus, in case of leakage, the pipe fills 1/7th part of the cistern in one hour.
Thus, in one hour due to leakage 1/42th part the cistern is emptied out.