PIPES AND CISTERNS

1.   INLET :-  The pipe connected to tank, that is used to fills it, is known as an inlet.

2.   OUTLET :-  The pipe connected to tank, that is used to emptying it, is known as an outlet.

3.   If a pipe can fill a tank in X hours , then the part filled in 1 hour,
                                                     
                                                               =$\frac{1}{X}$

4.   If a pipe can empty a tank in Y hours, then the part emptied in 1 hour,

                                                               =$\frac{1}{Y}$

5.   If a pipe A can fill a tank in X hours and a pipe B can fill the same tank in Y hours, then the net part filled in 1 hour, when both the pipes are opened

                                                               =$(\frac{1}{X}+\frac{1}{Y})$

6.   If a pipe A can fill a tank in X hours and a pipe B can empty the full tank in Y hours (where Y > X), then net part filled in 1 hour

                                                               =$(\frac{1}{X}-\frac{1}{Y})$

7.   If a pipe A can fill a tank in X hours and a pipe B can empty the full tank in Y hours (where X >Y), then net part emptied in 1 hour

                                                                =$(\frac{1}{Y}-\frac{1}{X})$

8.   If a pipe A fills a tank in X hours and another pipe B fills the same tank in Y hours but a third pipe C empties the full tank in Z hours, and if all of them are opened together, then net part filled in 1 hour
                                                               
                                                                =$(\frac{1}{X}+\frac{1}{Y}-\frac{1}{Z})$

                       $\therefore$ Time taken to fill the tank =$\frac{XYZ}{YZ+XZ-XY}$ hours