__Pipes and Cisterns__

__What is Inlet?__

Inlet: A Pipe is connected with tank and it fills with water or some liquid is called as Inlet.

__What is Outlet?__

Outlet: A Pipe connected with tank it emptying is called as an outlet.

__Remembering points of pipe examples:__

- If a pipe can fill a tank in x hours, then, part filled by 1 hours = .
- If a pipe can empty a tank in y hours, then, part emptied in 1 hours =
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y>x), then on opening both the pipes, the net part filled in 1 hours = ( – ).
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y>x), then on opening both the pipes, the net part emptied in 1 hours = ( – ).

__Example:__

Two pipes A and B can fill a tank in 12 hours and 14 hours respectively while a third pipe C empties the full tank in 30 hours.If all the A, B, C operate simultaneously, How much time will take be filled the tank?

__Answer:__

** Step 1:** Net part filled by 1 hour = ( + ) – = .

__Step 2:____The Time taken will fill the tank is = 8 hr 12 minutes.__

So time taken to fill the tank 8 hr 12 minutes.

__Example:__

Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are simultaneously, how much time will be taken to fill the tank?

__Answer:__

Here both pipes are working like a inlet,

__Step 1:____ __So at first of we calculate fill pipe in 1 hours time taken.

A + B together filled a tank in 1 hour = ( + ) = =

__Step 2:____ __So in 1 hour it fill with 1 / 20.

Hence time taken both the pipe A and B will fill the tank in 20 hours.

__Example:__

If A pipe can fill a tank in 12 hr. and pipes B can empty a tank in 20 hr. When both pipes are opened simultaneously, How much time will be taken to fill the tank?

__Answer:__

**Step 1:** At we calculate time taken to fill in hour hr and time taken to empty the a tank in hr.

**Step 2:** When both pipes are opened then time taken to fill

– = 5 –

=

So in 1 hour to take fill tank both are open A and B =

time taken when A and B are opened, A + B = = 30hr.

__Example:__

Pipes X fill the tank in 6 hours , Pipes Y fill the tank in 10 hours , Pipes Z fill the tank in 20 hours , If all the Pipes are open , in how many hours will the tank be filled ?

__Answer:__

Part filled by ( X + Y + Z ) in 1 hour = ( + + ) = .

So that All the three pipes together will fill the tank in 60 / 19hours.

__Example:__

There are two types Pipes, Pipes A and B can fill a tank in 3 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:

__Answer:____ __

Net part filled in 1 hour = ( + – ) = .

The tank will be full in hrs.

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