The topic of "Pipes and Cistern" is essential for students preparing for various school and competitive exams in India. Understanding this concept not only helps in grasping the underlying principles of fluid mechanics but also enhances problem-solving skills. Practicing MCQs and objective questions on this topic is crucial for effective exam preparation, as it allows students to familiarize themselves with important questions and improve their performance in exams.
What You Will Practise Here
Fundamentals of Pipes and Cisterns
Key formulas related to flow rates and capacities
Concepts of filling and emptying pipes
Real-life applications and examples
Diagrams illustrating pipe systems
Problem-solving techniques for complex scenarios
Commonly asked objective questions and their solutions
Exam Relevance
The topic of Pipes and Cistern is frequently included in the curriculum of CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that test their understanding of flow rates, the relationship between different pipes, and the time taken to fill or empty a cistern. Common question patterns include numerical problems, theoretical questions, and application-based scenarios that require critical thinking.
Common Mistakes Students Make
Confusing the rates of filling and emptying pipes
Neglecting to convert units when calculating flow rates
Misunderstanding the relationship between time, rate, and volume
Overlooking the impact of multiple pipes working simultaneously
FAQs
Question: What is the formula for calculating the time taken to fill a cistern? Answer: The time taken to fill a cistern can be calculated using the formula: Time = Volume / Rate of flow.
Question: How do I approach problems involving multiple pipes? Answer: First, determine the individual rates of each pipe, then combine them according to whether they are filling or emptying the cistern.
Now is the time to enhance your understanding of Pipes and Cistern! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is the key to success!
Q. If a tank is filled by a pipe in 5 hours and emptied by another pipe in 10 hours, how long will it take to fill the tank if both pipes are opened together?
A.
3 hours
B.
4 hours
C.
5 hours
D.
6 hours
Solution
The net rate is 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Q. If a tank is filled by a pipe in 6 hours and another pipe can empty it in 9 hours, how long will it take to fill the tank if both pipes are opened together?
A.
4 hours
B.
5 hours
C.
6 hours
D.
7 hours
Solution
The net rate is 1/6 - 1/9 = 3/18 - 2/18 = 1/18. Therefore, it will take 18 hours to fill the tank.
Q. If a tank is filled by a pipe in 7 hours and emptied by another pipe in 14 hours, how long will it take to fill the tank if both pipes are opened together?
A.
4 hours
B.
5 hours
C.
6 hours
D.
7 hours
Solution
The net rate is 1/7 - 1/14 = 2/14 - 1/14 = 1/14. Therefore, it will take 14 hours to fill the tank.
Q. If a tank is filled by two pipes A and B in 12 hours and 15 hours respectively, how long will it take to fill the tank if both pipes are opened together?
A.
6 hours
B.
7 hours
C.
8 hours
D.
9 hours
Solution
The combined rate is 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Therefore, it will take 20/3 hours or approximately 6.67 hours.
Q. If one pipe can fill a tank in 4 hours and another can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened together?
A.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
Solution
The combined rate is 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Therefore, it will take 12/5 hours or 2.4 hours.
Q. Pipe A can fill a tank in 15 hours, and pipe B can fill the same tank in 20 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
6 hours
B.
8 hours
C.
10 hours
D.
12 hours
Solution
The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours, approximately 8.57 hours to fill the tank.
Q. Pipe A can fill a tank in 15 hours, while pipe B can fill it in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
4 hours
B.
5 hours
C.
6 hours
D.
7 hours
Solution
The combined rate is 1/15 + 1/10 = 1/6. Therefore, it will take 6 hours to fill the tank.
Q. Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
Solution
The combined rate is 1/6 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Q. Two pipes can fill a tank in 10 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank?
A.
3 hours
B.
4 hours
C.
5 hours
D.
6 hours
Solution
The first pipe fills 1/2 of the tank in 5 hours. The remaining half can be filled by both pipes in 2 hours.
