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Pipes and cisterns problems are almost the same as those of Time and work problems. Thus, if a pipe fills a tank in 6 hrs, then the pipe fills 1/6th of the tank in 1 hr. the only difference with Pipes and Cisterns problems is that there are outlets as well as inlets. Thus, there are agents (the outlets) which perform negative work too. The rest of the process is almost similar.
INLET: An inlet pipe is connected with a tank and it fills tank.
OUTLET: A outlet pipe is connected with a tank and it empties tank.
Formulae
(i) If a pipe can fill a tank in m hrs, then the part filled in 1 hr =1/m.
(ii) If a pipe can empty a tank in n hrs, then the part of the full tank emptied in 1 hr = 1/n .
(iii) If a pipe can fill a tank in m hrs and the another pipe can empty the full tank in n hrs, then the net part filled in 1 hr, when both the pipes are opened =[1/m- 1/n]
∴ Time taken to fill the tank, when both the pipes are opened = mn/( n-m)
(iv) If a pipe can fill a tank in m hrs and another can fill the same tank in n hrs, then the net part filled in 1 hr, when both the pipes are opened = [1/n- 1/m]
∴ Time taken to fill the tank = mn/(n-m)
(v) If a pipe fills a tank in m hrs and another fills the same tank in n hrs, but a third one empties the full tank in p hrs, and all of them are opened together,
the net part filled in 1 hr = [1/m+ 1/n-1/p]
the net part filled in 1 hr = [1/m+ 1/n-1/p]
∴ Time taken to fill the tank =mnp/(np+mp-mn) hrs.
(vi) A pipe can fill a tank in m hrs. Due to a leak in the bottom it is filled in n hrs. if the tank is full, the time taken by the leak to empty the tank = mn/(n-m) hrs.
Example 1 : Two pipes P and Q can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened together, how much time will be taken to fill the tank?
Solution: 
Example 2 : A pipe can fill a tank in 25 hrs. Due to a leakage in the bottom, it is filled in 50 hrs. If the tank is full, how much time will the leak take to empty it?
Solution :
Example: Two pipes A and B can fill a tank in 16 minutes and 24 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that that the tank is full in 12 minutes?
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FAQs on Pipes and Cisterns - Concepts and Tricks - IBPS PO Prelims & Mains Preparation - Bank Exams
| 1. What are the basic concepts of pipes and cisterns? |  |
| 2. How do you solve problems related to pipes and cisterns in banking exams? | |
Ans. To solve problems related to pipes and cisterns in banking exams, you need to understand the basic concepts and formulas involved. You should be able to calculate the individual rates of different pipes, determine their combined rate when working together, and use this information to find the time taken to fill or empty a cistern. Practice solving different types of problems to improve your speed and accuracy.
| 3. What are the common tricks or shortcuts to solve pipes and cisterns problems quickly? | |
Ans. Here are some common tricks or shortcuts to solve pipes and cisterns problems quickly:
- Use the concept of efficiency: If a pipe fills a tank in x hours, its efficiency is 1/x. Similarly, if a pipe empties a tank in x hours, its efficiency is -1/x.
- When pipes work together, add their individual efficiencies to find the combined efficiency.
- When pipes work against each other, subtract their individual efficiencies to find the net efficiency.
- Use the concept of LCM (Least Common Multiple) to find the time taken to fill or empty the tank.
- Use the formula: Time = Volume / Efficiency to find the time taken.
| 4. Can you provide an example problem related to pipes and cisterns? | |
Ans. Sure, here's an example problem:
If Pipe A can fill a tank in 8 hours and Pipe B can empty the same tank in 12 hours, how long will it take to fill the tank if both pipes are open together?
Solution:
The efficiency of Pipe A = 1/8
The efficiency of Pipe B = -1/12
Combined efficiency = 1/8 - 1/12 = 1/24
Time taken = Volume / Combined efficiency
Let's assume the volume of the tank is 24 liters (a common multiple of 8 and 12).
Time taken = 24 / (1/24) = 24 * 24 = 576 hours.
Therefore, it will take 576 hours to fill the tank if both pipes A and B are open together.
| 5. How can I improve my speed and accuracy in solving pipes and cisterns problems for banking exams? | |
Ans. To improve your speed and accuracy in solving pipes and cisterns problems for banking exams, you can:
- Practice solving a variety of problems regularly to familiarize yourself with different problem types and techniques.
- Memorize the common formulas and shortcuts related to pipes and cisterns.
- Take timed mock tests or solve practice papers to simulate the exam environment and improve your speed.
- Analyze your mistakes and learn from them. Understand where you went wrong and find ways to avoid similar errors in the future.
- Seek guidance from teachers or mentors who can provide tips and strategies to solve pipes and cisterns problems more efficiently.
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