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Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. The number of hours taken by C alone to fill the cistern is
- a)12hrs
- b)10hrs
- c)18hrs
- d)8hrs
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Three pipes A, B and C can fill a cistern in 6 hours. After working at...
A+B+C in 1h = 1/6
A+B+C in 2h = 2/6 = 1/3
Remaining = 1-1/3 = 2/3
A+B in 6hrs = 2/3
A+B in 1hr = 2/18
C alone to fill the cistern = 1/6 – 2/18 = 3-2/18 = 1/18
A+B+C in 2h = 2/6 = 1/3
Remaining = 1-1/3 = 2/3
A+B in 6hrs = 2/3
A+B in 1hr = 2/18
C alone to fill the cistern = 1/6 – 2/18 = 3-2/18 = 1/18
Most Upvoted Answer
Three pipes A, B and C can fill a cistern in 6 hours. After working at...
A+B+C in 1h = 1/6
A+B+C in 2h = 2/6 = 1/3
Remaining = 1-1/3 = 2/3
A+B in 6hrs = 2/3
A+B in 1hr = 2/18
C alone to fill the cistern = 1/6 – 2/18 = 3-2/18 = 1/18
A+B+C in 2h = 2/6 = 1/3
Remaining = 1-1/3 = 2/3
A+B in 6hrs = 2/3
A+B in 1hr = 2/18
C alone to fill the cistern = 1/6 – 2/18 = 3-2/18 = 1/18
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Community Answer
Three pipes A, B and C can fill a cistern in 6 hours. After working at...
Given information:
- Pipes A, B, and C can fill a cistern in 6 hours when working together.
- After working together for 2 hours, pipe C is closed.
- Pipes A and B can fill the remaining part of the cistern in 6 hours.
Let's assume the rate at which pipe A can fill the cistern is "a", the rate at which pipe B can fill the cistern is "b", and the rate at which pipe C can fill the cistern is "c". We need to find the value of "c".
Rate of work formula:
Rate = Work done / Time
Total work done by the three pipes in 1 hour:
(a + b + c) * 1 = 1/6
After working together for 2 hours, the remaining work is (1 - (2/6)) = 4/6
Rate of work done by pipes A and B in 1 hour:
(a + b) * 1 = (4/6) / 6 = 2/9
Since the rate at which pipe A and B work together is 2/9, and the rate at which pipe A and B work together is (a + b), we can write the equation:
(a + b) = 2/9
Now, we can substitute the value of (a + b) in the equation (a + b + c) * 1 = 1/6:
(2/9 + c) * 1 = 1/6
Simplifying the equation:
2/9 + c = 1/6
c = 1/6 - 2/9
c = (3 - 4)/18
c = -1/18
Since time cannot be negative, the rate at which pipe C can fill the cistern is not -1/18. Therefore, there is an error in the given options.
- Pipes A, B, and C can fill a cistern in 6 hours when working together.
- After working together for 2 hours, pipe C is closed.
- Pipes A and B can fill the remaining part of the cistern in 6 hours.
Let's assume the rate at which pipe A can fill the cistern is "a", the rate at which pipe B can fill the cistern is "b", and the rate at which pipe C can fill the cistern is "c". We need to find the value of "c".
Rate of work formula:
Rate = Work done / Time
Total work done by the three pipes in 1 hour:
(a + b + c) * 1 = 1/6
After working together for 2 hours, the remaining work is (1 - (2/6)) = 4/6
Rate of work done by pipes A and B in 1 hour:
(a + b) * 1 = (4/6) / 6 = 2/9
Since the rate at which pipe A and B work together is 2/9, and the rate at which pipe A and B work together is (a + b), we can write the equation:
(a + b) = 2/9
Now, we can substitute the value of (a + b) in the equation (a + b + c) * 1 = 1/6:
(2/9 + c) * 1 = 1/6
Simplifying the equation:
2/9 + c = 1/6
c = 1/6 - 2/9
c = (3 - 4)/18
c = -1/18
Since time cannot be negative, the rate at which pipe C can fill the cistern is not -1/18. Therefore, there is an error in the given options.
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