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Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
  • a)
    6 hours
  • b)
    4 hours
  • c)
    2 hours
  • d)
    3 hours
Correct answer is option 'A'. Can you explain this answer?
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Two pipes A and B together can fill a cistern in 4 hours. Had they bee...
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Two pipes A and B together can fill a cistern in 4 hours. Had they bee...

Given Information:
- Together, pipes A and B can fill the cistern in 4 hours.
- If opened separately, pipe B takes 6 hours more than pipe A to fill the cistern.

Let's Assume:
- Let the time taken by pipe A to fill the cistern separately be x hours.
- Therefore, the time taken by pipe B to fill the cistern separately would be (x + 6) hours.

Calculations:
- The combined rate of pipes A and B = 1/4 cistern per hour (since they can fill the cistern in 4 hours together)
- The individual rate of pipe A = 1/x cistern per hour
- The individual rate of pipe B = 1/(x + 6) cistern per hour
- According to the given information, the sum of individual rates of A and B is equal to their combined rate:
1/x + 1/(x + 6) = 1/4
- Solving the above equation, we get:
(x + 6 + x) / (x(x + 6)) = 1/4
(2x + 6) / (x^2 + 6x) = 1/4
8x + 24 = x^2 + 6x
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x = 6 or x = -4

Conclusion:
- Since time cannot be negative, the time taken by pipe A to fill the cistern separately is 6 hours (option A).
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Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?a)6 hoursb)4 hoursc)2 hoursd)3 hoursCorrect answer is option 'A'. Can you explain this answer?
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