Fastest way to solve Aptitude problems, shortcuts, tricks and important formulas - Pipes and Cisterns:
Inlet: A
pipe connected with a tank or a cistern or a reservoir, that fills it, is known
as an inlet.
Outlet: A
pipe connected with a tank or a cistern or a reservoir, emptying it, is known
as an outlet.
1. If a pipe
can fill a tank in α hours, then: part filled in 1 hour = 1/α
2. If a pipe
can empty a full tank in β hours,
then: part emptied in 1 hour = 1/β
3. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where
β> α), then on
opening both the pipes,
The net part filled in 1 hour = (1/α) - (1/β)
The net part filled in 1 hour = (1/α) - (1/β)
4. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where α > β), then on
opening both the pipes,
The net part emptied in 1 hour = (1/β) - (1/α)
The net part emptied in 1 hour = (1/β) - (1/α)
Also, these shortcut formulas can be
used:
1. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where
β> α), then time
taken to fill the tank, when both the pipe are opened, αβ/(β - α)
2. If a pipe
can fill a tank in α hours and another pipe can fill the same tank in β hours,
then the net part the time taken to fill, when both the pipes are open
Time taken
to fill the tank = αβ/(α + β)
3. If a pipe
fills a tank in α hour and another fills the same tank in β hours, but a third
one empties the full tank in ɣ hours, and all of them are opened together, then
Time taken
to fill the tank = αβɣ/(βɣ +αɣ - αβ)
4. A pipe
can fill a tank in α hours. Due to a leak in the bottom, it is filled in β
hours. The time taken by the leak to empty the tank is, αβ/(β - α)
Example: 01
Two pipes A and B can fill the tank in 30
hrs and 45 hrs respectively. If both the pipes are opened simultaneously, how
much time will be taken to fill the tank?
Solution:
By 1st method;
A fills the
tank in 1 hr = 1/30 parts
B fills the
tank in 1 hr = 1/45 parts
A and B
together fills the tank in 1 hr = 1/30 + 1/45 = 1/18 parts
So, time
required to fill the tank is 18 hrs.
By 2nd method; Time taken = αβ/(α + β)
= (30 × 45)/(30 + 45) = 18 hrs.
Example: 02
Pipe A can fill a tank in 25 hrs while B
alone can fill it in 30 hrs and C can empty the full tank in 45 hrs. If all the
pipes are opened together, how much time will be needed to make the tank full?
Solution:
The tank
will be full in = (25 × 30 × 45)/[(30 × 45) + (25 × 45) - (25 × 30)] = 19.56
hours.
Example: 03
Two pipes A and B would fill a cistern in
24 hrs and 32 hrs respectively. If both the pipes are opened together; find
when the first pipe must be turned off so that the cistern may be just filled
in 16 hrs.
Solution:
B fills the
tank in 1 hr = 1/32 parts
B fills the
tank in 16 hrs = 16/32 parts = 1/2 part.
Given,
A fill the full
tank in 24 hrs
Therefore, A
fills the 1/2 part in just 12 hrs.
So, the
first pipe A should work for 12 hrs.
Alternate Method: The first should work
for = [1 - (16/32)] × 24 = 12 hrs.
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