# Formulas For Pipes & Cisterns

## Concepts of Pipes And Cisterns

As we all know that work and time is considered as one of the major topics of quantitative section for any competitive exam. Similarly, Pipes and Cisterns is major part of quantitative aptitude.  On this page we will see some of the major Formulas For Pipes and Cisterns.

### Definition of  Pipes & Cisterns

•  A pipe is connected to a tank or cistern to fill or empty the tank or cistern
• Inlet: A pipe which is connected to fill a tank is known as an inlet.
• Outlet: A pipe which is connected to empty a tank is known as an outlet.
• In pipes and cisterns problems – we need to find out what portion of the tank each of the pipes fill or drain in unit time (say in a minute or hour or second) and then perform arithmetic operation on this value.

### Formulas for Pipes and Cisterns

1. If pipe can fill a tank in x hours , then part filled in one hour = $\frac{1}{x}$

2. If pipe can empty a tank in y hours , then part emptied in one hour = $\frac{1}{y}$

3. If pipe A can fill a tank in x hours, Pipe B can empty the full tank in y hours (where y > x). Then, on opening both the pipes, the net part filled in one hour= $\frac{1}{x} – \frac{1}{y}$ OR $\frac{xy}{y-x}$ hours

4. If pipe A can fill a tank in x hours. Pipe B can empty the full tank in y hours (where x > y). Then, on opening both the pipes, the net part filled in one hour= $\frac{1}{y} – \frac{1}{x}$ OR $\frac{yx}{x-y}$ hours.

5. If pipe A can empty a tank in X hours. Pipe B can empty the same tank in Y hours. Then part of the tank emptied in one hour when both the pipes start working together = $\frac{1}{x} + \frac{1}{y}$

### Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

Questions for Pipes and Cisterns:

Question 1:  Tarun and Varun started a game in which they checked whose pipe fills the tank faster Tarun’s pipe A and  Varun’ s pipe B can fill a cistern in 6 hours and 8 hours, respectively. If both pipes are opened simultaneously, how long will they take to fill the cistern?

Answer:

Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/6 (fraction of the cistern filled per hour). The filling rate of Pipe B = 1/8 (fraction of the cistern filled per hour).

When both pipes are opened simultaneously, their filling rates are additive:

Combined filling rate = (1/6) + (1/8) = 7/24 (fraction of the cistern filled per hour).

Now, to find the time it will take to fill the cistern, we use the formula:

Time = 1 / Combined filling rate

Time = 1 / (7/24) = 24 / 7 ≈ 3.43 hours

Hence They will take approximately 3 hours and 26 minutes to fill the cistern when both pipes A and B are opened simultaneously.

Question 2: A tank has been connected to three pipes such that Pipe A can fill it in 4 hours, Pipe B in 6 hours, and Pipe C can empty it in 8 hours. If all pipes are opened at the same time, how long will it take to fill the tank wholly ?

Answer:

Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/4 (fraction of the tank filled per hour).

The filling rate of Pipe B = 1/6 (fraction of the tank filled per hour).

The emptying rate of Pipe C = -1/8

All three pipes are opened simultaneously, their net filling rate is the sum of the filling rates of Pipes A and B and the emptying rate of Pipe C:

Net filling rate = (1/4) + (1/6) + (-1/8) = 12/48 + 8/48 – 6/48 = 14/48 (fraction of the tank filled per hour).

Now, to find the time it will take to fill the tank, we use the formula:

Time = 1 / Net filling rate

Time = 1 / (14/48) = 48 / 14 ≈ 3.43 hours

Hence, It will take approximately 3 hours and 26 minutes to fill the tank completely when all three pipes A, B, and C are opened simultaneously

Question 3: Rajat and Raghav took two pipes Pipe A which can fill a cistern in 12 hours, and Pipe B  which can empty the cistern in 15 hours. If both pipes are opened together, how long will it take to fill the cistern?

Answer:
Let the total capacity of the cistern be C (considering 1 unit of capacity).

The filling rate of Pipe A = 1/12 (fraction of the cistern filled per hour). The emptying rate of Pipe B = -1/15 (negative value since it is emptying, and we consider emptying as a negative filling rate).

When both pipes are opened simultaneously, their net filling rate is the sum of the filling rate of Pipe A and the emptying rate of Pipe B:

Net filling rate = (1/12) + (-1/15) = 5/60 – 4/60 = 1/60 (fraction of the cistern filled per hour).

Now, to find the time it will take to fill the cistern, we use the formula:

Time = 1 / Net filling rate

Time = 1 / (1/60) = 60 hours

Hence,  It will take 60 hours to fill the cistern when both pipes A and B are opened simultaneously.

## Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others