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Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?
  • a)
    2 hours
  • b)
    1 hour 45 minutes
  • c)
    2 hour 11 minutes
  • d)
    2 hour 10 minutes
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two pipes, when working one at a time, can fill a cistern in 3 hours a...
Understanding the problem:
Given:
- Pipe 1 fills the cistern in 3 hours
- Pipe 2 fills the cistern in 4 hours
- Pipe 3 empties the cistern in 8 hours
- When all three pipes are opened together, the cistern was 1/12 full

Approach to solving the problem:
To find out the time taken for the cistern to be completely full when all three pipes are opened together, we need to calculate the net amount of water filled in the cistern per hour.

Calculating the net amount of water filled per hour:
- Pipe 1 fills 1/3 of the cistern in an hour
- Pipe 2 fills 1/4 of the cistern in an hour
- Pipe 3 empties 1/8 of the cistern in an hour
Therefore, the net amount of water filled per hour when all three pipes are opened together is:
(1/3 + 1/4 - 1/8) = (8 + 6 - 3) / 24 = 11 / 24

Calculating the time taken to fill the cistern completely:
Since the cistern was 1/12 full when all three pipes were opened together, it needs to be filled with 11/12 of the water.
Time taken to fill 11/12 of the cistern = (11/12) / (11/24) = 24 / 2 = 12 hours
Therefore, the cistern will be completely full in 12 hours.

Conclusion:
The correct answer is option 'A' which is 2 hours.
Free Test
Community Answer
Two pipes, when working one at a time, can fill a cistern in 3 hours a...
Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)
Work done by pipe 1 in 1 hour = 24/3 = 8 units.
Work done by pipe 2 in 1 hour = 24/4 = 6 units.
Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units
Total work done in 1 hour = 8 + 6 – 3 = 11 units
The time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours
∴ The correct answer is 2 hours.
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Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?a)2 hoursb)1 hour 45 minutesc)2 hour 11 minutesd)2 hour 10 minutesCorrect answer is option 'A'. Can you explain this answer?
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Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?a)2 hoursb)1 hour 45 minutesc)2 hour 11 minutesd)2 hour 10 minutesCorrect answer is option 'A'. Can you explain this answer? for CLAT 2024 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?a)2 hoursb)1 hour 45 minutesc)2 hour 11 minutesd)2 hour 10 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CLAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?a)2 hoursb)1 hour 45 minutesc)2 hour 11 minutesd)2 hour 10 minutesCorrect answer is option 'A'. Can you explain this answer?.
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