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A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?
- a)167 minutes
- b)155 minutes
- c)180 minutes
- d)165 minutes
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A, B and C are three pipes attached to a cistern. A and B can fill the...
LCM of 15, 20 and 30 is 60.
Let the capacity of tank be 60 liters.
A and B fill the tank at a rate of 3 liters per minute and 2 liters per minute, respectively. C empties the tank at a rate of 4 liters per minute.
If opened successfully for 1 minute each, 1 liter will be filled in 3 minutes.
So, 55 liters will be filled in 55 × 3 = 165 minutes
After the 165th minute, tap A and B will fill the left capacity of 5 liters in 2 minutes.
So, the total time taken = 167 minutes
Let the capacity of tank be 60 liters.
A and B fill the tank at a rate of 3 liters per minute and 2 liters per minute, respectively. C empties the tank at a rate of 4 liters per minute.
If opened successfully for 1 minute each, 1 liter will be filled in 3 minutes.
So, 55 liters will be filled in 55 × 3 = 165 minutes
After the 165th minute, tap A and B will fill the left capacity of 5 liters in 2 minutes.
So, the total time taken = 167 minutes
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A, B and C are three pipes attached to a cistern. A and B can fill the...
Understanding the Problem:
The problem involves three pipes - A, B, and C attached to a cistern. Pipe A can fill the cistern in 20 minutes, pipe B can fill it in 30 minutes, and pipe C can empty it in 15 minutes. The task is to determine how soon the cistern will be filled if pipes A, B, and C are kept open successively for 1 minute each.
Calculating the Efficiency of Each Pipe:
- Pipe A fills the cistern in 20 minutes, so its efficiency is 1/20.
- Pipe B fills the cistern in 30 minutes, so its efficiency is 1/30.
- Pipe C empties the cistern in 15 minutes, so its efficiency is -1/15 (negative because it empties the cistern).
Calculating the Combined Efficiency:
When all three pipes are open successively for 1 minute each, the net efficiency for each cycle is (1/20 + 1/30 - 1/15) = 1/60.
Calculating the Total Time:
Since the combined efficiency is 1/60, the time taken to fill the cistern is the reciprocal of this value, which is 60 minutes.
However, since the pipes are opened successively for 1 minute each, the cistern will be filled in 60 * 3 = 180 minutes.
Therefore, the cistern will be filled in 180 minutes.
Conclusion:
The correct answer is option (c) 180 minutes.
The problem involves three pipes - A, B, and C attached to a cistern. Pipe A can fill the cistern in 20 minutes, pipe B can fill it in 30 minutes, and pipe C can empty it in 15 minutes. The task is to determine how soon the cistern will be filled if pipes A, B, and C are kept open successively for 1 minute each.
Calculating the Efficiency of Each Pipe:
- Pipe A fills the cistern in 20 minutes, so its efficiency is 1/20.
- Pipe B fills the cistern in 30 minutes, so its efficiency is 1/30.
- Pipe C empties the cistern in 15 minutes, so its efficiency is -1/15 (negative because it empties the cistern).
Calculating the Combined Efficiency:
When all three pipes are open successively for 1 minute each, the net efficiency for each cycle is (1/20 + 1/30 - 1/15) = 1/60.
Calculating the Total Time:
Since the combined efficiency is 1/60, the time taken to fill the cistern is the reciprocal of this value, which is 60 minutes.
However, since the pipes are opened successively for 1 minute each, the cistern will be filled in 60 * 3 = 180 minutes.
Therefore, the cistern will be filled in 180 minutes.
Conclusion:
The correct answer is option (c) 180 minutes.
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A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer?
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A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer?.
A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C are three pipes attached to a cistern. A and B can fill the cistern respectively in 20 and 30 minutes, while C can empty the cistern in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?a)167 minutesb)155 minutesc)180 minutesd)165 minutesCorrect answer is option 'A'. Can you explain this answer?.
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