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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?
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Verified 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
∴ Time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours
Most Upvoted 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
∴ Time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours
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Two pipes, when working one at a time, can fill a cistern in 3 hours a...
Given:
- Pipe A can fill the cistern in 3 hours
- Pipe B can fill the cistern in 4 hours
- Pipe C can drain the cistern in 8 hours
- All three pipes were opened together when the cistern was 1/12 full
Let's find the rate at which each pipe fills or drains the cistern:
- Pipe A fills 1/3 of the cistern per hour (since it fills the cistern in 3 hours)
- Pipe B fills 1/4 of the cistern per hour (since it fills the cistern in 4 hours)
- Pipe C drains 1/8 of the cistern per hour (since it drains the cistern in 8 hours)
To find the combined rate at which the three pipes fill or drain the cistern, we need to consider the net rate:
- When all three pipes are open, the net rate is equal to the sum of the individual rates.
- Since Pipe A and Pipe B are filling the cistern, their rates are positive.
- Since Pipe C is draining the cistern, its rate is negative.
Let's define the positive net rate as R:
R = (1/3 + 1/4) - 1/8 = 7/24
Now, let's determine the time it takes for the cistern to be completely full using the concept of work done:
- The work done by the net rate R is equal to the difference in the initial and final levels of the cistern.
- The initial level is 1/12 full, and the final level is completely full.
- The work done by the net rate R is equal to the final level minus the initial level.
Let the time taken for the cistern to be completely full be T:
Work done by R in time T = 1 - 1/12
Since the work done is equal to the rate multiplied by time, we can write the equation as:
R * T = 1 - 1/12
Substituting the value of R, we get:
(7/24) * T = 1 - 1/12
Simplifying the equation, we get:
(7/24) * T = 11/12
Cross-multiplying, we get:
T = (11/12) * (24/7) = 22/7 = 3.14 hours
Converting 0.14 hours to minutes, we get:
0.14 * 60 = 8.4 minutes
Therefore, the cistern takes approximately 3 hours and 8.4 minutes to be completely full, which is closest to option A (2 hours).
- Pipe A can fill the cistern in 3 hours
- Pipe B can fill the cistern in 4 hours
- Pipe C can drain the cistern in 8 hours
- All three pipes were opened together when the cistern was 1/12 full
Let's find the rate at which each pipe fills or drains the cistern:
- Pipe A fills 1/3 of the cistern per hour (since it fills the cistern in 3 hours)
- Pipe B fills 1/4 of the cistern per hour (since it fills the cistern in 4 hours)
- Pipe C drains 1/8 of the cistern per hour (since it drains the cistern in 8 hours)
To find the combined rate at which the three pipes fill or drain the cistern, we need to consider the net rate:
- When all three pipes are open, the net rate is equal to the sum of the individual rates.
- Since Pipe A and Pipe B are filling the cistern, their rates are positive.
- Since Pipe C is draining the cistern, its rate is negative.
Let's define the positive net rate as R:
R = (1/3 + 1/4) - 1/8 = 7/24
Now, let's determine the time it takes for the cistern to be completely full using the concept of work done:
- The work done by the net rate R is equal to the difference in the initial and final levels of the cistern.
- The initial level is 1/12 full, and the final level is completely full.
- The work done by the net rate R is equal to the final level minus the initial level.
Let the time taken for the cistern to be completely full be T:
Work done by R in time T = 1 - 1/12
Since the work done is equal to the rate multiplied by time, we can write the equation as:
R * T = 1 - 1/12
Substituting the value of R, we get:
(7/24) * T = 1 - 1/12
Simplifying the equation, we get:
(7/24) * T = 11/12
Cross-multiplying, we get:
T = (11/12) * (24/7) = 22/7 = 3.14 hours
Converting 0.14 hours to minutes, we get:
0.14 * 60 = 8.4 minutes
Therefore, the cistern takes approximately 3 hours and 8.4 minutes to be completely full, which is closest to option A (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 SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC 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 SSC 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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