Pipe and Cistern

Pipes and cisterns are essential to quantitative ability in various aptitude exams. The concept relates to the flow of liquids and their applications. The concepts of time and work are also required while solving these problems.

What are pipes and cisterns?

Pipes and cistern related problems generally consisted of two parts –

• Cistern: Also known as a tank, a cistern is usually used to store water. A cistern has an inlet and an outlet to store or drain water.

• Pipes: Pipes are hollow cylinders for water flow from one point to another. Pipes are connected to a cistern to drain the liquid out of or fill the liquid into the cistern. Pipes are of 2 types:

  • Inlet pipe: Inlet pipes are used to fill the cistern with liquids.

  • Outlet pipe: Outlet pipes are used to drain the cistern.

Essential formulas for pipes and cisterns

Here are some of the essential formulas used in Pipes and Cisterns related problems.

• If the tank must be drained in y hours, the part drained in 1 hour = 1/y

• If filling a tank takes x hours, it can be partly full in 1 hour = 1/x

• (Sum of work completed by Inlets) – (Net work done) (Sum of work done by Outlets)

• If a pipe fills a cistern in x hours and empties it in y hours, and both pipes are used at the same time, the net portion of the tank will be filled in 

  • 1 hour = (xy) / (x – y), assuming x > y

  • 1 hour = (xy) / (y – x), assuming y>x

• If two inlets are allowed at the same time, and one inlet can fill the tank in x hours, and the other inlet can fill the tank in y hours, 

the time taken to fill the entire tank = (xy) / (y+x).

• If two pipes fill a tank with water in x and y hours, respectively, and a third pipe is opened to empty the tank in z hours, 

  • the time taken to fill the tank = 1 / (1/x)+(1/y)+(1/z), and 

  • the net portion of the tank filled in 1 hr = (1/x)+(1/y)-(1/z).

Easy tricks to solve the pipes and cistern related problems

Here are a few pointers to assist candidates in easily and quickly completing word problems involving pipelines and cisterns:

• Inlet, outlet, leak, refilling, draining a tank, and the formulas associated with these concepts must all be understood. Only then will a candidate be aware of the topic without becoming perplexed.

• If you can’t answer the question, make sure you don’t spend too long on a single question.

• Remember the formulae and practise them as much as possible to understand the idea better.

Solved Examples

1. A cistern can be filled in 20 minutes and 30 minutes by two pipes, A and B, respectively and emptied in 40 minutes by a third pipe, C. How long would it take to fill the cistern when all three pipes are released simultaneously?

Solution: Calculating the time required to fill each part we get.

Part of the tank filled or emptied = 1/t 

=> Part of the tank filled by inlet pipe A in 1 min = 1/20

=> Part of the tank filled by inlet pipe B in 1 min = 1/30

=> Part of the tank emptied by outlet pipe C in 1 min = 1/40

Using the formula: (Sum of work completed by Inlets) – (Net work done) (Sum of work done by Outlets)

1/20 + 1/30 – 1/40 = 7/120

Here, pipe C empties the tank, denoted as -ve, while pipe A and B values are denoted as +ve.

Therefore, in mixed fractions,

=>120/7 = 17 1/7

      2.   Three pipelines, X, Y, and Z, require 6 hours to fill a tank. Z was closed after the three operated together for two hours, and X and Y finished the remaining tank in seven hours. How long will it take Z to fill up the tank by himself?

Solution: 1/3 of the tank that was filled in 2 hours.

The remaining portion of the tank to be filled = 1 – 1/3 = 2/3

Work completed by X and Y in 7 hours = 2/3

Therefore time taken by X and Y to fill the tank 

= 7 * 3/2 = 10.5 hrs

Z’s 1 hour’s work = (1/6)-(1/10.5) = (10.5–6)/63 = 4.5/63 = (1/14)

Hence, the time taken by Z to fill the tank alone will be 14 hrs.

      3.   Two-fifths of a water reservoir is filled. In ten minutes, Pipe A can load a tank, and Pipe B can empty it in six minutes. How long will it take to completely drain or fill the tank if both lines are open?

Solution: Pipe B is quicker than pipe A. Hence the tank will be empty.

2/5 part to be emptied section empty in 1 minute by (A+B) = (1/6 – 1/10) = 1/15

= 1/15 : 2/5 : 1 : x

= 2/5 * 15 = 6 mins

As a result, the tank will be empty in 6 minutes.

Conclusion

Pipes and cisterns are important concepts and are used in day to day life. The time and speed of water flowing from one point to another are calculated using the concepts of pipes and cisterns. It is important to remember the formulas and use them accurately, depending on any pipe and cistern-related problems’ inlet and outlet.