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Pipes Emptying and Filling The Tank

Pipe And Cistern - Concepts

Single Pipe Emptying The Tank

Single Pipe Filling The Tank

Multiple Pipes Filling The Tank

Pipes Emptying and Filling The Tank

Solving Statements Involving Pipes

Class - Railways Subjects

Concept Explanation

Pipes Emptying And Filling The Tank

Pipes and Cisterns

Pipes are connected to tank or reservoir, or cisterns are used to fill or empty the tank.

Inlet

A pipe or a tap connected with a tank ( or a cistern or a reservoir) is called an inlet, if it fills it.

Outlet

A pipe or a tap connected with a tank (or a cistern or a reservoir) is called an outlet, if it empties it.

Pipes Emptying And Filling The Tank:

Let us consider a situation in which more than one pipe is connected to a tank or a reservoir and is either filling or emptying it. The pipe or tap which is filling are the inlet to the tank or reservoir. The pipe or tap which is emptying are the outlet to the tank or reservoir.

We will first calculate the part of tank filled by the pipe connected as inlet in 1 hour.

Similarly We will calculate the part of tank emptied by the pipe connected as outlet in 1 hour

Finally we will subtract the fraction emptied from the fraction filled in 1 hour.

We will then take the reciprocal to find the total time taken by all the pipes together to fill the tank

Formula:

Let us consider the case when one pipes filling and the other emptying the tank together

If 1st pipe can fill a tank in x h,

Then the part filled by the 1st pipe in 1 h can be calculated as

$Part ;filled ;by;1st ;pipe ;in; 1 ;h=frac{1}{x}$

Similarly, if 2nd pipe can empty a tank in y h,

Then the part emptied by the 2nd pipe in 1 h can be calculated as

$Part ;emptied ;by;2nd ;pipe ;in; 1 ;h=frac{1}{y}$

Then the part filled by the both the pipes in 1 h can be calculated as the difference of the part filled and emptied by individual pipe

$Part ;filled ; by;both;the;pipes;together; in; 1 ;h=frac{1}{x} -frac{1}{y}=frac{y-x}{xy}$

To calculate the time taken to fill the tank by both the pipes together. we will take the reciprocal of the part filled in one hour

$=frac{xy}{y-x}$

Illustration: A cistern can be filled by a tap in 12 hours and emptied by the other tap in 15 hours. If both taps are opened together how long will it take to fill the cistern?

A. 30 B. 20 C. 60 D. 45

Answer: C

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Sample Questions

(More Questions for each concept available in Login)

Question : 1

If a pipe can fill a tank in 7 h and another pipe can empty the full tank in 13 h, then how long will it take to fill the tank, if both the pipes are opened together ?
A. $fn_phv 15frac{1}{8} h$	B. $14frac{1}{7} h$	C. $17frac{1}{6} h$	D. $15frac{1}{6} h$
Right Option : D
View Explanation

Question : 2

A cistern normally takes 10 hours to be filled by a tap but because of one open outlet pipe, it takes 5 hours more. In how many hours will the outlet pipe will empty a full cistern?
A. 20 hours	B. 24 Hours	C. 30 Hours	D. None of these
Right Option : C
View Explanation

Question : 3

A tank is three - fourth full. Pipe A can fill the tank in 12 min. Pipe B can empty it in 8 min. If both pipes are open, how long will it take to empty the tank ?
A. 18 min	B. 17 min	C. 16 min	D. 15 min
Right Option : A
View Explanation