Pipes & Cisterns: Theory & Concepts

Questions on Pipes and Cisterns are almost like Time and Work questions. This is a very simple topic yet very important topic from exam point of view as questions on this topic are commonly asked in Campus Recruitment Tests, Banks Entrance Exams, Management Entrance Tests and Other Competitive Exams. Doing lot of practice on this topic can help you in getting good exposure and you should be able to solve all the questions asked on this very topic.
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In this article, we will go through the basic concepts, important formulas and Pipes and Cistern tricks and shortcuts along with frequently asked questions on pipes and cisterns, and learn approaches to solve these questions quickly.
In pipes and cisterns problems – we need to find out what portion of the tank each of the pipes fill or drain in unit time (say in a minute / hour / second) and then perform arithmetic operation on this value.
Say Pipe A can fill a tank in 10 hrs and Pipe B can empty a full tank in 15 hrs. Now assuming the capacity of the tank to be 30 litres, A fills 30/10 = 3 litres in an hour and B drains 30/15 = 2 litres in an hour. The net inflow in the tank after one hour is 3 – 2 = 1 litre. So, the tank will be filled in 30/1 = 30 hrs.
Basic Concepts and Pipes & Cisterns formulae used in this topic:
INLET: An inlet is a pipe which is connected to the tank and with the help of this pipe, the tank is filled.
OUTLET/LEAK: An outlet is a pipe which is connected to the tank. This pipe drains out water from the tank and the tank gets emptied if this pipe is opened.
Formulae
  1. If a pipe can fill a tank in a hrs, then the part filled in 1 hr =1/a.
  2. If a pipe can empty a tank in b hrs, then the part of the full tank emptied in 1 hr = 1/b.
  3. If a pipe can fill a tank in a hrs and the another pipe can empty the full tank in b hrs, then the net part filled in 1 hr, when both the pipes are opened =[1/a - 1/b] ∴ Time taken to fill the tank, when both the pipes are opened = ab/(b - a)
  4. If a pipe can fill a tank in a hrs and another can fill the same tank in b hrs, then the net part filled in 1 hr, when both pipes are opened = [1/a + 1/b] ∴ Time taken to fill the tank = ab/(a + b)
  5. If a pipe fills a tank in a hrs and another fills the same tank in b hrs, but a third one empties the full tank in c hrs, and all of them are opened together, the net part filled in 1 hr = [1/a+ 1/b-1/c] ∴ Time taken to fill the tank =abc/(bc + ac – ab) hrs.
  6. A pipe can fill a tank in a hrs. Due to a leak in the bottom it is filled in b hrs. If the tank is full, the time taken by the leak to empty the tank = ab/(b - a) hrs.
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