Pipes and cistern problems

In the pipes and cistern problems, the majority of the problems deals with Inflow,outflow,current capacity, full tank,empty tank.
There will be few inlets connected to a dam or tank through which water enters into dam or tank and outlet through which water exits the tank or dam.
cistern: A tank to store water.

Important points.

1. If pipe can fill the tank in 'x' hours then rate of flow is 1/x(1/x portion of tank gets filled in 1 hour)(when we divide the tank into x parts,one part gets filled in a unit of time)
2. If pipe can empty the tank in 'y' hours then emptying rate is 1/y(1/y portion of tank gets emptied in 1 hour)

The rate at which tank is filling =rate of inflow - the rate of outflow.

If a pipe fills the tank at 1/x rate and another pipe empties the tank in 1/y rate then on opening both the pipes :

• If (x<y) rate at which tank is  is 1/x-1/y
• If (x>y) rate at which tank is emptying is 1/y-1/x

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Pipes and cisterns solved problems:
Example 1:

If there are two inlets for dam (namely A,B) and an outlet (namely C)

A alone can make the dam full in 5 months,B alone can fill the dam in 4 months and C alone can make the full dam empty in 20 months,how many months are needed to make the empty dam full when all the three (A,B,C)are kept open.

solution:

Rate of filling(R)=rate of  inflows - rate of outflows.

R=(1/5+1/4)-1/20
R=0.4=4/10
As Rate=1/Time.
No.of months:10/4=2.5

Example 2:
Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively,how much time would the tank needs to become full when both the pipes are kept open.
solution:
given data:
Rate at which A fills the tank=1/20 (1/20 th part of tank gets filled in 1 minute)
Rate at which B fills the tank=1/30 (1/30 th part of tank gets filled in 1 minute)
Rate of filling(R)=rate of inflows-rate of outflows
R=1/20+1/30
R=1/12
Rate=1/Time
so Time =12 minutes.

Example 3:
A tap A can fill a tank in 6 hours is kept open,when half the tank is filled three more similar taps are kept open,how much time does it take to fill entire tank.
solution:
Rate at which A can fill the tank=1/6
split the problem into 2 modules
module1>As full tank needs 6 hours, the half tank gets filled in three hours.
module2>To fill the second half ,three more similar taps are kept open(total 4 taps) rate
at which tank gets filled is 4(1/6)=2/3
Time=1/rate
Time required to fill the tank=3/2=1.5 hours=90 minutes
 Time required to fill the half tank=90/2=45 minutes
Total time required:3hours 45 minutes

Example 4:
If a car's fuel tank has a capacity of 50 liters and when the fuel is filled at a rate of 22 liters/hr,and the owner of fuel filling station wanted to cheat and he took back 2 liters/hr back through the same pipe what is the time required to make the empty tank full.
solution:
Rate of filling= Rate of inflows - Rate of outflows
Rate of filling = 22-2=20 liters/hour (40 liters/2 hours) (50 liters/2.5 hours)
If 20 liters/hour rate is maintained,the total required time=2.5 hours.


Feel free to comment if you have any queries or modifications.