In this section we will discuss about PIPES AND CISTERNS.

In most questions, Pipes are connected to a tank or cistern and are used to fill or empty the tank or cistern. In pipe and cistern, the work is done in the form of filling or emptying a cistern/tank.

Inlet pipe: It fills a tank/cistern/reservoir.

Outlet pipe: It empties a tank /cistern /reservoir.

Generally, time taken to fill a tank is taken positive and time taken to empty a tank is taken as negative.

Let’s take an example,

E.g. An outlet pipe can fill a cistern in 5 h. in what time will the pipe fill 2/5 part of the cistern?

Solution:  

⸪ Time taken to fill full cistern = 5 h

∴ time taken to fill 2/5 cistern would be 2/5 times less than usual

⇒ 2/5 × 5 = 2 h. (Ans.)

We saw it is a thing of common sense, right.

We will try to use the minimum number of formulas to make it easy as it could be.

E.g. If a pipe can fill a tank in 2 h and another pipe can fill the same tank in 6 h, then what part

of a tank will be filled by both the pipes in 1 h, if they are opened simultaneously?

Solution :

In 1 h , part filled by 1^st pipe would be = ½ ;

In 1 h , part filled by 2^nd pipe would be = 1/6;

So both of them fill the pipe together = ( ½  + 1/6)

⇒ ½  + 1/6 = 4/6 = 2/3 part (Ans.)

Now let’s talk about the most famous type of question of pipes and cisterns, you might see this in any exam like SBI PO.

E.g. Two pipes A and Bcan fill a tank in 18 h and 12 h, respectively. If both the pipes are

opened simultaneously, how much time will be taken to fill the tank?

Solution:

Part filled by A in 1 h = 1/18

Part filled by B in 1 h = 1/12

Doing similarly as we did in last example

total part filled by A & B together = (1/18 + 1/12)

⇒ 1/18 + 1/12 = 5/36 part

Let the number of hours in which A & B finish filling = x

We know that total of all parts would be 1

⇒  x × 5/36 = 1

⇒ x = 36/5 = 7 hour and 12 minutes (Ans.)

Here we observe that the total time taken is inverse of part done in 1 h.

Till now we studied pipes and combinations of pipes and how much do they take to finish the filling, what if the outlet pipe is added to this combination?

Let’s try to find out.

E.g. A pipe can fill a tank in 5 h, while another pipe can empty it in 6 h. If both the pipes are

opened simultaneously, how much time will be taken to fill the tank?

Solution:

 Here one pipe is filling the tank and one is emptying the tank so it would take greater time than usual.

Part filled by inlet pipe in 1 h = 1/5

Part filled by outlet pipe in 1 h = – 1/6

Part of the outlet pipe would be negative because there done work is undone.

Total part fill by both in 1 h = 1/ 5 – 1/6

⇒ 1/5 – 1/6  = 1/30

⇒ Total time in filling the tank = 30 h

This method will be faster as well as more interesting.

Let’s try to learn with the same examples;

(First, go to percentages for better understanding of this method)

E.g. An outlet pipe can fill a cistern in 5 h. In what time will the pipe fill the 2/5 part of the cistern?

Let’s look at this example with a different point of view

The pipe can fill the cistern in 5 hours completely (100%) so in one hour it would fill 1/5 or 20%.

2/5 part would be in 40%

⇒ So 40% be filled in 2 hours. (Ans.)

It seems odd to use here but in a complicated situation, this method would be more useful.

E.g. A pipe can fill a tank in 5 h, while another pipe can empty it in 6 h. If both the pipes are

opened simultaneously, how much time will be taken to fill the tank?

Here efficiency of the first pipe would be 1/5 or 20% (fill in 1 hour)

And the efficiency of the second pipe would be -1/6 = -16.67% (hope you remember our table in percentages unit)

So net efficiency would be = 20.00 – 16.67 = 3.33%

So number of days would be = 100/3.33 = 30 (Ans.)