Saturday 22 March 2014

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 Methods

Pipes and Cisterns Shortcut Methods


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
xy/(y-x) hours 

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.