### Pipes and Cistern

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__Pipes & Cisterns__

Important points :

1.

2.

3. A pipe takes x hours to fill up the tank. Then

4. A pipe takes y hours to empty the tank. Then part emptied in 1 hour =

5. Pipe A can fill a tank n times as fast as another pipe B. This means:

**Inlet Pipe**A pipe which fills up the tank is known as inlet.

2.

**Outlet Pipe**A pipe which empties the tank is known as outlet.

3. A pipe takes x hours to fill up the tank. Then

x

1

parts of the tank will be filled in 1 hour.4. A pipe takes y hours to empty the tank. Then part emptied in 1 hour =

y

1

5. Pipe A can fill a tank n times as fast as another pipe B. This means:

i) If slower pipe B takes x min to fill up the empty tank,then faster pipe A takes

ii) If they operate together, then part of the tank that is filled up in 1 hour is (n + 1)/x

6. Let a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours. We can examine two cases here. n

x

min to fill up the empty tank.
ii) If they operate together, then part of the tank that is filled up in 1 hour is (n + 1)/x

i) x < y

In this case, the net part filled in 1 hour =

ii) y < x

In this case, the net part emptied in 1 hour =

In this case, the net part filled in 1 hour =

x

1

- y

1

ii) y < x

In this case, the net part emptied in 1 hour =

y

1

- x

1