Pipes and Cistern

Pipes and Cistern

A pipe is used to fill or empty the tank or cistern.

Inlet Pipe
A pipe used to fill the tank or cistern is known as Inlet Pipe.

Example sum
Two pipes A and B can fill a tank in 20 and 30 min respectively. If both the pipes are used together, then how long will it take to fill the tank?
Part filled by A in 1 min = 1 / 20
Part filled by B in 1 min = 1 / 30
Part filled by (A + B) in 1 min = [(1/ 20 )+ (1/30)]

=(3+2)/60

=5/60
=1/12

Outlet Pipe
A pipe used to empty the tank or cistern is known as Outlet Pipe.

Example sum
A cistern can be filled by a tap in 4 hr while it can be emptied by another tap in 9hr. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Net part filled in 1 hr = (1/4)-(1 / 9)
=(9-5)/36
=5/36
The cistern will be filled in 36 / 5 hrs or 7.2 hrs

Inlet and Outlet Pipes base 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= (1 / x) -(1 / y)

Problem solve shortcut method
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)] hrs ( or) [(1/x)+(1/y))

Example sum 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?
Part filled by A in 1 min = 1 / 20
Part filled by B in 1 min = 1 / 30
Part filled by (A + B) in 1 min = (1 / 20 ) +(1/30)
=(3+2)/60

=5/60
=1/12
Both pipes can fill the tank in 12 minutes.

Problem solve shortcut method
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 )

Example sum
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?
Part filled by (A + B + C ) in 3 minutes 

= 3*[(1/30)+(1/20)+(1/10)]

=3*[(2+3+6)/60]

=(3*(11/60))
= 33 / 60
= 11 / 20
Part filled by C in 3 minutes = 3/10
Required ratio (3/10)*(20 / 11 )
=6/11

Problem solve shortcut method
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 one hr = [ (1/x)+(1/y)]-(1/z)
Time taken to fill full cistern = (xyz ) / (yz+xz - xy)

Example sum
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 find the tank will be filled?
Net part filled in 1 hour =(1/5)+ (1 / 6)-(1/12)
= 17 / 60
The tank will be full in ( 60 / 17 ) hours
=[3*(9/17)]hours

Problem solve shortcut method
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)] hrs

Example sum
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. Find the leak can drain all the water of the tank ?

Work done by the leak in 1 hour= (1/2)-(3/7)
=(7-6)/14

=1/14
Leak will empty the tank in 14 hrs.