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 tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?
A.
8 hours
B.
10 hours
C.
12 hours
D.
14 hours
Solution
In 4 hours, A fills 1/3 of the tank. The remaining 2/3 can be filled by A and B together in 4 hours.
Q. A tank is filled by two pipes A and B in 15 hours and 20 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
A.
8 hours
B.
10 hours
C.
12 hours
D.
15 hours
Solution
The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours to fill the tank.
Q. A tank is filled by two pipes A and B in 15 hours and 25 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
A.
9 hours
B.
10 hours
C.
12 hours
D.
15 hours
Solution
The combined rate is 1/15 + 1/25 = 2/15. Therefore, it will take 15/2 = 7.5 hours to fill the tank.
Q. A tank is filled by two pipes 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.
2 hours
B.
3 hours
C.
4 hours
D.
5 hours
Solution
The first pipe fills 1/10 * 5 = 1/2 of the tank. The remaining 1/2 can be filled by both pipes together in 2 hours.
Q. A tank is filled by two pipes in 12 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 completely?
A.
6 hours
B.
7 hours
C.
8 hours
D.
9 hours
Solution
In 5 hours, the first pipe fills 5/12 of the tank. The remaining is 1 - 5/12 = 7/12. The combined rate of both pipes is 1/12 + 1/15 = 7/60. Therefore, it will take (7/12) / (7/60) = 60/12 = 5 hours to fill the remaining part.
Q. A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first pipe is opened for 3 hours and then the second pipe is opened, how long will it take to fill the tank?
A.
5 hours
B.
6 hours
C.
7 hours
D.
8 hours
Solution
In 3 hours, the first pipe fills 3/9 = 1/3 of the tank. The remaining 2/3 can be filled by both pipes in 2 hours.
Q. If a cistern is filled by two pipes A and B in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
A.
6 hours
B.
7.2 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 6.67 hours.
Q. If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
A.
6 hours
B.
7.2 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 6.67 hours.
Q. If a pipe can fill a tank in 20 hours and another pipe can empty it in 25 hours, how long will it take to fill the tank if both pipes are opened together?
A.
50 hours
B.
100 hours
C.
80 hours
D.
40 hours
Solution
The net rate is 1/20 - 1/25 = 1/100. Therefore, it will take 100 hours to fill the tank.
Q. If a pipe can fill a tank in 20 minutes and another pipe can empty it in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
A.
10 minutes
B.
15 minutes
C.
20 minutes
D.
25 minutes
Solution
The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 minutes to fill the tank.
Q. If a pipe can fill a tank in 24 hours and another pipe can empty it in 30 hours, how long will it take to fill the tank if both pipes are opened together?
A.
120 hours
B.
60 hours
C.
80 hours
D.
40 hours
Solution
The net rate is 1/24 - 1/30 = 1/120. Therefore, it will take 120 hours to fill the tank.
Q. If a pipe can fill a tank in 25 minutes and another pipe can empty it in 50 minutes, how long will it take to fill the tank if both pipes are opened together?
A.
15 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. If a pipe can fill a tank in 9 hours and another pipe can fill it in 6 hours, how long will it take to fill the tank if both pipes are opened together?
A.
3.6 hours
B.
4 hours
C.
4.5 hours
D.
5 hours
Solution
The combined rate is 1/9 + 1/6 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.
Q. If a tank can be filled by a pipe in 15 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.
5 hours
B.
6 hours
C.
7 hours
D.
8 hours
Solution
The net rate is 1/15 - 1/10 = 2/30 - 3/30 = -1/30. Therefore, the tank will never fill.
Q. If a tank can be filled by a pipe in 20 hours and emptied by another pipe in 30 hours, how long will it take to fill the tank if both pipes are opened together?
A.
12 hours
B.
15 hours
C.
18 hours
D.
24 hours
Solution
The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 hours to fill the tank.
Q. If a tank can be filled by a pipe in 20 minutes and emptied by another pipe in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
A.
10 minutes
B.
15 minutes
C.
20 minutes
D.
25 minutes
Solution
The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 minutes to fill the tank.
Q. If a tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes, how long will it take to fill the tank if both pipes are opened together?
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. If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 hours, how long will it take to fill the tank if both pipes are opened together?
A.
1.5 hours
B.
2 hours
C.
2.5 hours
D.
3 hours
Solution
The combined rate is (1/3 - 1/5) = (5-3)/15 = 2/15. Therefore, it will take 15/2 hours or 7.5 hours.
Q. If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 9 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 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. If a tank can be filled by a pipe in 4 hours and emptied by another pipe 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 net rate is 1/4 - 1/6 = 3/12 - 2/12 = 1/12. Therefore, it will take 12 hours to fill the tank.
Q. If a tank can be filled by a pipe in 6 hours and another pipe can empty it in 4 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 net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. Therefore, the tank will never fill.
Q. If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 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 net rate is 1/6 - 1/4 = 2/12 - 3/12 = -1/12. Therefore, the tank will never fill.
Q. If a tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 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 combined rate is (1/6 - 1/9) = (3-2)/18 = 1/18. Therefore, it will take 18 hours to fill the tank.
Q. If a tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours, how long will it take to fill the tank if both pipes are opened together?
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. If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?
A.
1 hour
B.
2 hours
C.
3 hours
D.
4 hours
Solution
In 2 hours, the filling pipe fills 2/5 of the tank and the emptying pipe empties 2/10 of the tank. Net filled = 2/5 - 1/5 = 1/5. Therefore, 1/5 of the tank is filled.
