Pipes and Cisterns Shortcut Methods
Pipe and Cistern problems are similar to time and work problems. A pipe is used to fill or empty the tank or cistern.
What is Inlet Pipe: A pipe used to fill the tank or cistern is known as Inlet Pipe.
What is Outlet Pipe: A pipe used to empty the tank or cistern is known as Outlet Pipe.
Pipes and Cisterns Shortcut Formulas
Pipes and Cisterns Formula 1:
Two pipes can fill (or empty) a cistern in x and y hours while working alone. If both pipes are opened together, then the time taken to fill (or empty) the cistern is given by (xy/(x+y)) hours
Pipes and Cisterns Formula 2:
Three pipes can fill (or empty) a cistern in x, y and z hours while working alone. If all the three pipes are opened together, the time taken to fill (or empty) the cistern is given by (xyz/(xy+yz+zx))hours
Pipes and Cisterns Formula 3:
If a pipe can fill a cistern in x hours and another can fill the same cistern in y hours, but a third one can empty the full tank in z hours, and all of them are opened together, then
Net Part filled in 1 hour = 1/x + 1/y - 1/z
Time taken to fill the full cistern = xyz/(yz+xz-xy)
Pipes and Cisterns Formula 4:
A pipe can fill a cistern in x hours. Because of a leak in the bottom, it is filled in y hours. If it is full, the time taken by the leak to empty the cistern is
Pipes and Cisterns basic formulas:
If an inlet pipe can fill the tank in x hours, then the part filled in 1 hour = 1/x
If an outlet pipe can empty the tank in y hours, then the part of the tank emptied in 1 hour = 1/y
If both inlet and outlet valves are kept open, then the net part of the tank filled in 1 hour is 1/x-1/y
Pipes and Cisterns Question 1
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Step1: Take L.C.M for 20 and 30
Step2: Tank capacity (L.C.M) is 60
Every min pipe A fill 3 part of the tank (60/20=3)
Every min pipe B fill 2 part of the tank (60/30=2)
Together filling so (3+2=5) 5 part of the tank is filling at Every min 12*5=60
Totally 60(L.C.M) parts will be fill in 12 minutes
Pipes and Cisterns Question 2
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
Ans : 6/11
Pipes and Cisterns Question 3
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Ans : 60/17 Hours
Pipes and Cisterns Question 4
A pipe can fill a tank in 3 hours. Because of leak in the bottom, it is filled in 4 hours. If the tank is full, how much time will the leak take to empty it?
Pipes and Cisterns 1/3-1/4 =1/12
So leak will empty the tank in 12 hours.
(Apply this formula xy/(y-x) ans 12 hours)
Pipes and Cisterns Problem 5
Two pipes A and B can fill a tank in 15 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 ?
Solution :Part of tank filled by A + B in 1 minute = ( 1 / 15 + 1 / 20 )
So tank filled by A + B in 4 minute = 4 ( 1 / 15 + 1 / 20 ) = 7 / 15
Part remaning = 1 - ( 7 / 15 ) = 8 / 15
1 / 20 part is filled by B in 1 minute
So, 8 / 15 part will be filled in = ( 20 / 1 )* ( 8 / 15 ) = 32 / 3 = 10 minutes 40 sec.
Pipes and Cisterns Problem 6
A cistern is normally filled in 8 hrs, but it takes four hrs longer to fill beacuse of a leak in the bottom. If the cistern is full , how much time the leak will empty it ?
Solution : Let the leak will empty the tank in x hrs.
Then part of cistern filled in 1 hr = ( 1 / 8 ) - ( 1 / x ) = x - 8 / 8x
So cistern will completly filled in 8x / x – 8
Ans : 24 hours
Pipes and Cisterns Problem 7
A tank is normally filled in 8 hrs. but takes 2 hrs.longer to fill because of leak in its bottom. If the cistern is full, in how many hours will the leak empty it?
Solution: When leak doesn’t work the tank is filled in 8 hrs.
When both filler pipe and leak work together, the tank is filled in 8+2 = 10 hrs.
Therefore, the time taken by leak to empty the tank = 8*10/ (10-8) = 40 Hours
Pipes and Cisterns Problem 8
A tank has a leak which would empty it in 8 hrs. A tap is turned on which admits 6 liters a minute in to the tank, and it is now emptied in 12 hrs. How many liters does the tank hold?
Solution: The time taken to fill the tank 12*8/(12-8) = 24 hours
Pipes and Cisterns Problem 9
An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 (1/2)hours to fill the tank. If the tank is full, how much time will the leak take to empty it ?
Work done by the leak in 1 hour =[(1/3)-(1/(7/2))=1/3-7/2=1/21
The leak will empty the tank in 21 hours.