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Pipe and Cisterns

The same principle of Time and Work is employed to solve the problems on Pipes and Cisterns. The only difference is that in this case, the work done is in terms of filling or emptying a cistern (tank) and the time taken is the time taken by a pipe or a leak (crack) to fill or empty a cistern respectively.
 
Inlet : A pipe connected with a tank (or a cistern or a reservoir) is called an inlet, if it fills it.
 
Outlet : A pipe connected with a tank is called an outlet, if it empties it.
  • If a pipe can fill a tank in x hours, then the part filled in 1 hour Description: 568.png
  • If a pipe can empty a tank in y hours, then the part of the full tank emptied in 1 hour Description: 573.png.
  • If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then the net part filled in 1 hour, when both the pipes are openedDescription: 578.png.
     
     Time taken to fill the tank, when both the pipes are openedDescription: 583.png.
  • If a pipe can fill a tank in x hours and another can fill the same tank in y hours, then time taken to fill the tank Description: 588.png, when both the pipes are opened
  • 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 net part filled in 1 hr Description: 593.png
     
     Time taken to fill the tank Description: 598.png hours.
  • 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 is given by Description: 604.png minutes.




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