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Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?
  • a)
    110 minutes
  • b)
    100 minutes
  • c)
    120 minutes
  • d)
    90 minutes
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Two pipes A and B can separately fill a cistern in 60 minutes and 75 m...
Work done by the third pipe in 1 min. = 1/50 - ( 1/60 + 1/75 )
= ( 1/50 - 3/100 )
= - 1/100
Therefore, the third pipe alone can empty the cistern in 100 min
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Most Upvoted Answer
Two pipes A and B can separately fill a cistern in 60 minutes and 75 m...
To solve this problem, we can use the concept of work.

Let's assume the capacity of the cistern is C liters.

Pipe A can fill the cistern in 60 minutes, so its work rate is C/60 liters per minute.
Pipe B can fill the cistern in 75 minutes, so its work rate is C/75 liters per minute.
When all three pipes are opened, they fill the cistern in 50 minutes, so their combined work rate is C/50 liters per minute.

Let's assume the third pipe can empty the cistern in T minutes, so its work rate is -C/T liters per minute (negative sign because it is emptying the cistern).

Now, let's calculate the combined work rate of all three pipes.

Combined work rate = work rate of pipe A + work rate of pipe B + work rate of the third pipe

C/50 = C/60 + C/75 - C/T

Now, let's simplify this equation and solve for T.

Multiplying through by 150 (common multiple of denominators):

3C = 2C + 1.5C - 150C/T

Combining like terms:

3C = (2C + 1.5C) - 150C/T

3C = 3.5C - 150C/T

Subtracting 3C from both sides:

0.5C = -150C/T

Dividing both sides by C:

0.5 = -150/T

Cross-multiplying:

T = -150/0.5

T = -300

Since time cannot be negative, we discard the negative solution.

Therefore, the third pipe alone can empty the cistern in 300 minutes.

The correct answer is option B) 100 minutes.
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Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?a)110 minutesb)100 minutesc)120 minutesd)90 minutesCorrect answer is option 'B'. Can you explain this answer?
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Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?a)110 minutesb)100 minutesc)120 minutesd)90 minutesCorrect answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?a)110 minutesb)100 minutesc)120 minutesd)90 minutesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes A and B can separately fill a cistern in 60 minutes and 75 minute respectively. There is a third pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 minutes. In how much time can the third pipe alone empty the cistern?a)110 minutesb)100 minutesc)120 minutesd)90 minutesCorrect answer is option 'B'. Can you explain this answer?.
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