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. A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the cistern?
A.
4 hours
B.
6 hours
C.
8 hours
D.
10 hours
Solution
The net rate is 1/8 - 1/12 = 3/24 - 2/24 = 1/24. Therefore, it will take 24 hours to fill the cistern.
Q. A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
5 hours
B.
6 hours
C.
7 hours
D.
8 hours
Solution
The net rate of filling the tank is 1/10 - 1/15 = 1/30. Therefore, it will take 30 hours to fill the tank.
Q. A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 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 net rate is 1/12 - 1/8 = 1/24. Therefore, it will take 24 hours to fill the tank.
Q. A pipe can fill a tank in 5 hours, and a second pipe can fill the same tank in 10 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 1/5 + 1/10 = 3/10. Therefore, it will take 10/3 hours or 3.33 hours to fill the tank.
Q. A tank can be filled by a pipe in 10 hours and emptied by another pipe in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
5 hours
B.
6 hours
C.
10 hours
D.
12 hours
Solution
The net rate is 1/10 - 1/15 = 1/30. Therefore, it will take 30 hours to fill the tank.
Q. A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
10 hours
B.
5 hours
C.
15 hours
D.
20 hours
Solution
The net rate is 1/10 - 1/5 = -1/10. Therefore, the tank will never fill.
Q. A tank can be filled by a pipe in 12 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
10 hours
B.
12 hours
C.
15 hours
D.
18 hours
Solution
The net rate is 1/12 - 1/18 = 1/36. Therefore, it will take 36 hours to fill the tank.
Q. A tank can be filled by a pipe in 15 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
30 hours
B.
20 hours
C.
25 hours
D.
15 hours
Solution
The net rate is 1/15 - 1/10 = -1/30. Therefore, the tank will never fill.
Q. A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
10 hours
B.
12 hours
C.
15 hours
D.
18 hours
Solution
The net rate is 1/15 - 1/20 = 4/60 - 3/60 = 1/60. Therefore, it will take 60 hours to fill the tank.
Q. A tank can be filled by a pipe in 15 hours and emptied by another pipe in 25 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
10 hours
B.
12 hours
C.
15 hours
D.
20 hours
Solution
The net rate is 1/15 - 1/25 = 1/75. Therefore, it will take 75 hours to fill the tank.
Q. A tank can be filled by a pipe in 25 hours and emptied by another pipe in 50 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
16.67 hours
B.
20 hours
C.
25 hours
D.
30 hours
Solution
The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 hours to fill the tank.
Q. A tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes. If both pipes are opened together, how long will it take to fill the tank?
A.
16.67 minutes
B.
20 minutes
C.
25 minutes
D.
30 minutes
Solution
The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 minutes to fill the tank.
Q. A tank can be filled by a pipe in 3 hours and emptied by another pipe in 6 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 net rate is 1/3 - 1/6 = 2/6 - 1/6 = 1/6. Therefore, it will take 6 hours to fill the tank.
Q. A tank can be filled by a pipe in 3 hours and emptied by another pipe 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 net rate is 1/3 - 1/9 = 3/9 - 1/9 = 2/9. Therefore, it will take 9/2 hours or 4.5 hours.
Q. A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 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 net rate is 1/4 - 1/6 = 1/12. Therefore, it will take 12 hours to fill the tank.
Q. A tank can be filled by a pipe in 4 hours and emptied by another pipe in 8 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 net rate is 1/4 - 1/8 = 2/8 - 1/8 = 1/8. Therefore, it will take 8 hours to fill the tank.
Q. A tank can be filled by a pipe in 40 minutes and emptied by another pipe in 60 minutes. If both pipes are opened together, how long will it take to fill the tank?
A.
20 minutes
B.
30 minutes
C.
40 minutes
D.
50 minutes
Solution
The net rate is 1/40 - 1/60 = 1/120. Therefore, it will take 120 minutes to fill the tank.
Q. A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
3 hours
B.
4 hours
C.
5 hours
D.
6 hours
Solution
The net rate is 1/5 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Q. A tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 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 net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.
Q. A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
3.6 hours
B.
4 hours
C.
5 hours
D.
6 hours
Solution
The net rate is 1/6 - 1/9 = 1/18. Therefore, it will take 18 hours to fill the tank.
Q. A tank can be filled by a pipe in 7 hours and emptied by another pipe in 14 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 net rate is 1/7 - 1/14 = 2/14 - 1/14 = 1/14. Therefore, it will take 14 hours to fill the tank.
Q. A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
4 hours
B.
6 hours
C.
8 hours
D.
10 hours
Solution
The net rate is 1/8 - 1/12 = 3/24 - 2/24 = 1/24. Therefore, it will take 24 hours to fill the tank.
Q. A tank can be filled by a pipe in 9 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
6 hours
B.
9 hours
C.
12 hours
D.
15 hours
Solution
The net rate is 1/9 - 1/18 = 1/18. Therefore, it will take 18 hours to fill the tank.
Q. A tank can be filled by a pipe in 9 hours and emptied by another pipe in 3 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
2.25 hours
B.
3 hours
C.
4.5 hours
D.
5 hours
Solution
The net rate is 1/9 - 1/3 = 1/9 - 3/9 = -2/9. Therefore, the tank will never fill.
Q. A tank has two pipes, one fills it in 5 hours and the other empties it in 10 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 net rate is 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Q. A tank has two pipes, one fills it in 5 hours and the other empties it in 10 hours. If both 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 net rate is 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.
Q. A tank has two pipes. Pipe A can fill it in 6 hours and pipe B can empty it in 4 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 net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. The tank will never fill as the emptying rate is greater.
Q. A tank has two pipes. Pipe A can fill the tank in 6 hours, and pipe B can empty it in 4 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 net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. Therefore, the tank will never fill.
Q. A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
A.
4 hours
B.
6 hours
C.
8 hours
D.
10 hours
Solution
The net rate is 1/8 - 1/12 = 1/24. Therefore, it will take 24 hours to fill the tank.
Q. A tank is filled by two pipes A and B in 10 hours and 15 hours respectively. 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 1/10 + 1/15 = 3/30 + 2/30 = 5/30. Therefore, it will take 30/5 hours or 6 hours.
