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Pipe and Cistern Tips and Tricks for Government Exams

Theory

Pipes and cisterns problems are almost the same as those of Time and work problems. Thus, if a pipe fills a tank in 6 hrs, then the pipe fills 1/6th of the tank in 1 hr. the only difference with Pipes and Cisterns problems is that there are outlets as well as inlets. Thus, there are agents (the outlets) which perform negative work too.
Pipe and Cistern Tips and Tricks for Government Exams

Formula

  • If x hours are required to fill up a tank, then part filled in 1 hr =1/x
  • If y hours are required to empty the tank, then part emptied in 1 hour = 1/y
  • If a pipe can fill a tank in x hours and can empty the same tank in y hours. When both the pipes are opened at the same time, then the net part of the tank filled in 1 hr = {(xy) / (y-x)}, provided y>x
  • If a pipe can fill a tank in x hours and can empty the same tank in y hours. When both the pipes are opened at the same time, then the net part of the tank filled in 1 hr = {(xy) / (x-y)}, provided x>y
  • Net work done = (Sum of work done by Inlets) – (Sum of work done by Outlets)
  • One inlet can fill the tank in x hr and the other inlet can fill the same tank in y hrs, if both the inlets are opened at the same time, the time taken to fill the whole tank = {(xy) / (y+x)}
  • If two pipes take x and y hours respectively to fill a tank of water and a third pipe is opened which takes z hours to empty the tank, then the time taken to fill the tank = {1 / (1/x)+(1/y)+(1/z)} and the net part of the tank filled in 1 hr = (1/x)+(1/y)-(1/z)

Tips

  • One must be familiar with terms like inlet, outlet, leak, filling a tank, emptying a tank and the formulas related to the same. Only then can a candidate answer these questions without getting confused
  • If you are unable to crack the question, then ensure that you do not spend too much time on a single question 
  • Memorize the formulas and practise as much as possible to understand the concept better

Solved Examples

Question for Tips & Tricks: Pipe & Cistern
Try yourself:

Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the cistern is

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Question for Tips & Tricks: Pipe & Cistern
Try yourself:

Pipes A and B can fill a tank in 5 and 3 hrs respectively. Pipe C can empty empty it in 15 h. The tank is half full. All the three pipes are in operation simultaneously. After how much time the tank will be full ?

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Question for Tips & Tricks: Pipe & Cistern
Try yourself:

Two pipes A and B can fill a tank in 10 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, Pipe A is turned off. What is the total time required to fill the tank ?

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