Pipes and Cistern - Important Points
Questions based on pipes and cistern is asked in all competitive exams. The concept of time and work will be applied to solve questions from this topic.
Pipes and Cistern Formula
With 1 Inlet pipe: If a pipe can fill a tank in x hours, then the part of tank filled in 1 hour = 1 / x
With 2 inlet pipe: If a pipe can fill a tank in x hours and another fill the same tank in y hours, then the net part filled in 1 hr, when both pipes are opened: 1/x + 1/y
Time taken to fill the tank = xy/(x + y)
With 1 inlet and 1 outlet pipe: 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 opened = 1/x – 1/y
Time taken to fill the tank, when both the pipes are opened = xy/(y – x)
With 3 inlet pipes: If a pipe fills a tank in x hrs and another fills the same tank in y hrs, but a third empties the full tank in z hrs and all of them are opened together, the net part filled in 1 hr = 1/x + 1/y + 1/z
Time taken to fill the tank = xyz/(yz + xz - xy)
Pipes and Cistern problem types
A. When some inlet pipes opened together
B. First pipe open and second pipe open after some time
C. Some pipes opened for some time then few of them closed
Let’s understand this with the help of an example.
Example: Pipe A can fill a tank in 10 hrs, pipe B can fill it in 15 hrs. In what time, the tank will be full if-
(a) If both are opened together
(b) First pipe A is opened and pipe B is opened after 4 hrs
(c) If both are opened for 2 hrs, then pipe A is closed
(d) If both the pipe are opened alongwith a third outlet pipe C, which cam empty a filled tank in 20 hrs
Solution: Total capacity of tank = LCM (10,15,20) = 60 Ltr
Fill Rate (ltr/hr)
A 60/10 = 6
B 60/15 = 4
C 60/20 = -3 (for question d)
(a) Both can fill the tank in = 60/(6 + 4) = 6 hrs
(b) In 4 hrs, A filled 24 ltr
Remaining capacity = 60 – 24 = 36 ltr
B can fill it in = 36/4 = 9 hrs
Total time to fill = 4 + 9 = 13 hrs
(c) In 2 hrs, 2 x (6 + 4) = 20 ltr is filled
Remaining capacity = 40 ltr
B can fill this in = 40/4 = 10 hrs
Total time to fill = 2 + 10 = 12 hrs
(d) In 1 hr, All can fill 6 + 4 – 3 = 7 ltr
The tank will be filled in = 60/7 = 8 4/7 hrs