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__Fastest way to solve Aptitude problems, shortcuts, tricks and important formulas - Pipes and Cisterns__:

__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 Î± hours, then: part filled in 1 hour = 1/Î±

2. If a pipe
can empty a full tank in Î²

*hours, then: part emptied in 1 hour = 1/Î²*
3. If a pipe
can fill a tank in Î± hours and another pipe can empty the full tank in Î² hours (where
Î²> Î±),

The net part filled in 1 hour = (1/Î±) - (1/Î²)

*then on opening both the pipes,*The net part filled in 1 hour = (1/Î±) - (1/Î²)

4. If a pipe
can fill a tank in Î± hours and another pipe can empty the full tank in Î² hours (where Î± > Î²), then on
opening both the pipes,

The net part emptied in 1 hour = (1/Î²) - (1/Î±)

The net part emptied in 1 hour = (1/Î²) - (1/Î±)

__Also, these shortcut formulas can be used:__
1. If a pipe
can fill a tank in Î± hours and another pipe can empty the full tank in Î² hours (where
Î²> Î±),

*then time taken to fill the tank, when both the pipe are opened, Î±Î²/(Î² - Î±)*
2. If a pipe
can fill a tank in Î± hours and another pipe can fill the same tank in Î² hours,
then the net part the time taken to fill, when both the pipes are open

Time taken
to fill the tank = Î±Î²/(Î± + Î²)

3. If a pipe
fills a tank in Î± hour and another fills the same tank in Î² hours, but a third
one empties the full tank in É£ hours, and all of them are opened together, then

Time taken
to fill the tank = Î±Î²É£/(Î²É£ +Î±É£ - Î±Î²)

4. A pipe
can fill a tank in Î± hours. Due to a leak in the bottom, it is filled in Î²
hours. The time taken by the leak to empty the tank is, Î±Î²/(Î² - Î±)

__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 = Î±Î²/(Î± + Î²) = (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.

**Pipes and Cisterns:**

**Formula: Pipes and Cisterns Formulas**

**Solved Examples: Solved Examples: Set 01**

**Practice Test: Practice Test: 01**

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