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Pipes and Cisterns

Aptitude

Pipes and Cisterns -> IMPORTANT FACTS AND FORMULAE

Inlet : A pipe connected with a tank or a certain or a reservoir, that fills it, is known as an inlet.
Outlet : A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.
I. If a pipe can fill a tank in x hours, then :
part filled in 1 hour = 1 / x.
II. If a pipe can fill a tank in y hours, then :
part emptied in 1 hour = 1 / y.
III. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours(where y > x), then on opening both the pipes, the net part filled in 1 hour = (1/x - 1/y).
IV. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours(where x > y), then on opening both the pipes, the net part emptied in 1 hour = (1/y - 1/x).

Pipes and Cisterns -> SOLVED EXAMPLES

1. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
  Sol. Part filled by A in 1 hour = 1 / 36;
Part filled by B in 1 hour = 1 / 45;
Part filled by (A + B) in 1 hour = (1 / 36 + 1 / 45) = 9 / 180 = 1 / 20.

Pipes and Cisterns -> EXERCISE

4. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
 
  • A. 4.5 hrs
  • B. 5 hrs
  • C. 6.5 hrs
  • D. 7.2 hrs
Ans: D.
Sol.
Net part filled in 1 hour = (1/4 - 1/9)= 5/36.
∴ The cistern will be filled in 36/5 hrs i.e. 7.2 hrs.
 
5. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
 
  • A. 2
  • B. 2.5
  • C. 3
  • D. 3.5
Ans: C.
Sol.
Part filled by (A + B + C) in 1 hour = (1/5 + 1/10 + 1/30) = 1/3.
∴ All the three pipes together will fill the tank in 3 hours.
 
 
6. Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?
 
  • A. 5 hrs
  • B. 8 hrs
  • C. 9 hrs
  • D. 36 hrs
Ans: D.
Sol.
Part filled by ( A + B ) in 1 hour = [1/5 + 1/20] = 1/4.
So, A and B together can fill the tank in 4 hours.
Work done by the leak in 1 hour = (1/4 - 2/9) = 1/36.
∴ Leak will empty the tank in 36 hrs.