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Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 5 hours to fill up the whole tank. After how many hours Q was closed?
  • a)
    14 hours
  • b)
    15 hours
  • c)
    10 hours
  • d)
    16 hours
  • e)
    None of the Above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two pipes P and Q can fill a cistern in 10 hours and 20 hours respecti...
Pipe P Efficiency = 100/10 = 10%
Pipe Q Efficiency = 100/20 = 5%
Net Efficiency = 15%
15x + 10(5-x) = 100
x = 10
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Most Upvoted Answer
Two pipes P and Q can fill a cistern in 10 hours and 20 hours respecti...
Given Data:
- Pipe P can fill the cistern in 10 hours
- Pipe Q can fill the cistern in 20 hours
- Both pipes are opened simultaneously initially
- It takes a total of 5 hours to fill the cistern after tap Q was closed

Calculating the rate of filling:
- The rate of filling of pipe P = 1/10 cisterns per hour
- The rate of filling of pipe Q = 1/20 cisterns per hour
- Combined rate of filling when both pipes are open = 1/10 + 1/20 = 3/20 cisterns per hour

Let x be the time taken for tap Q to be closed:
- Therefore, the cistern was filled by both pipes for x hours and then by pipe P alone for (5 - x) hours
- The work done by both pipes in x hours + work done by pipe P in (5 - x) hours = 1 cistern

Solving the equation:
- (3/20) * x + (1/10) * (5 - x) = 1
- 3x + 2(5 - x) = 20
- 3x + 10 - 2x = 20
- x = 10

Conclusion:
- Tap Q was closed after 10 hours. Therefore, option C - 10 hours is the correct answer.
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Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 5 hours to fill up the whole tank. After how many hours Q was closed?a)14 hoursb)15 hoursc)10 hoursd)16 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?
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