Rule  Description 

1  If a pipe can fill a tank in x hours, then the part filled in 1 hour = \[\frac{1}{x}\] 
2  If a pipe can empty a tank in y hours, then the part of the full tank emptied in 1 hour = \[\frac{1}{y}\] 
3  If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then

4  If a pipe can fills or empties tank in x hours and another can fill or empties the same tank in y hours, then time taken to fill or empty the tank, when both pipes are opened = \[\frac{xy}{y+x}\] 
5  If a pipe fills a tank in x hours and another fills the same tank is y hours, but a third one empties the full tank in z hours, and all of them are opened together, then

6  A pipe can fill a tank in x hrs. Due to a leak in the bottom it is filled in y hrs. If the tank is full, then Time taken by the leak to empty the tank = \[\frac{xy}{yx}\] hrs. 
7  A cistern has a leak which can empty it in X hours. A pipe which admits Y litres of water per hour into the cistern is turned on and now the cistern is emptied in Z hours. Then The capacity of the cistern = \[\frac{x+y+z}{zx}\] litres. 
8  Two filling pipes A and B opened together can fill a cistern in t minutes. If the first filling pipe A alone takes X minutes more or less than t and the second fill pipe B along takes Y minutes more or less than t minutes, then \[t=\sqrt{xy}\] minutes. 
9  If one filling pipe A is n times faster and takes X minutes less time than the other filling pipe B, then the time they will take to fill a cistern,

10  A cistern is filled by three pipes whose diameters are X cm, Y cm, and Z cm. respectively (where X <Y <Z). Three pipes are running together. If the largest pipe Z alone will fill it in P minutes and the amount of water flowing in by each pipe is proportional to the square of its diameter, then the time in which the cistern will be filled by the three pipes is = \[\left[\frac{pz^2}{x^2+y^2+z^2}\right]\] minutes. 