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Two pipes can fill a cistern separately in 10 hours and 15 hours. They can together fill the cistern in
- a)9 hours
- b)6 hours
- c)7 hours
- d)8 hours
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two pipes can fill a cistern separately in 10 hours and 15 hours. They...
Understanding the Problem
To solve the problem of how long two pipes can fill a cistern together, we start by determining their individual filling rates.
Individual Filling Rates
- Pipe A can fill the cistern in 10 hours. Therefore, its rate is 1/10 cisterns per hour.
- Pipe B can fill the cistern in 15 hours. Hence, its rate is 1/15 cisterns per hour.
Combined Filling Rate
To find the combined rate of both pipes, we add their individual rates:
- Combined rate = Rate of Pipe A + Rate of Pipe B
- Combined rate = 1/10 + 1/15
To perform this addition, we need a common denominator. The least common multiple of 10 and 15 is 30.
- 1/10 = 3/30
- 1/15 = 2/30
Now, adding these rates:
- Combined rate = 3/30 + 2/30 = 5/30 = 1/6
Time to Fill the Cistern Together
The combined rate of 1/6 means that together, the two pipes can fill 1 cistern in 6 hours.
Conclusion
The correct answer is option 'B', as the two pipes working together can fill the cistern in 6 hours.
To solve the problem of how long two pipes can fill a cistern together, we start by determining their individual filling rates.
Individual Filling Rates
- Pipe A can fill the cistern in 10 hours. Therefore, its rate is 1/10 cisterns per hour.
- Pipe B can fill the cistern in 15 hours. Hence, its rate is 1/15 cisterns per hour.
Combined Filling Rate
To find the combined rate of both pipes, we add their individual rates:
- Combined rate = Rate of Pipe A + Rate of Pipe B
- Combined rate = 1/10 + 1/15
To perform this addition, we need a common denominator. The least common multiple of 10 and 15 is 30.
- 1/10 = 3/30
- 1/15 = 2/30
Now, adding these rates:
- Combined rate = 3/30 + 2/30 = 5/30 = 1/6
Time to Fill the Cistern Together
The combined rate of 1/6 means that together, the two pipes can fill 1 cistern in 6 hours.
Conclusion
The correct answer is option 'B', as the two pipes working together can fill the cistern in 6 hours.
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Community Answer
Two pipes can fill a cistern separately in 10 hours and 15 hours. They...
Using Rule 1,
Part of the cistern filled by both pipes in 1 hour
The cistern will be filled in 6 hours.
Part of the cistern filled by both pipes in 1 hour
The cistern will be filled in 6 hours.
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