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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...
Given:
Time taken by pipe A to fill the cistern = 60 minutes
Time taken by pipe B to fill the cistern = 75 minutes
Time taken by all three pipes to fill the cistern = 50 minutes

To find:
Time taken by the third pipe alone to empty the cistern

Approach:
Let's assume that the capacity of the cistern is 1 unit.
In 1 minute, pipe A can fill 1/60th of the cistern.
In 1 minute, pipe B can fill 1/75th of the cistern.
In 1 minute, all three pipes together can fill 1/50th of the cistern.

Calculation:
Let's assume that the third pipe can empty the cistern in x minutes.
In 1 minute, the third pipe can empty 1/xth of the cistern.

Now, let's calculate the net amount of water filled in the cistern in 1 minute when all three pipes are opened together:

Net amount of water filled = Amount of water filled by pipe A + Amount of water filled by pipe B - Amount of water emptied by the third pipe
= 1/60 + 1/75 - 1/x

Given that the net amount of water filled by all three pipes together is 1/50th of the cistern in 1 minute:

1/50 = 1/60 + 1/75 - 1/x

To solve this equation, we need to find the value of x.

Simplifying the equation:

1/50 = (5/300) + (4/300) - 1/x
1/50 = 9/300 - 1/x
1/50 = (9 - 1/x) / 300
1/50 = (9x - 1) / (300x)

Cross-multiplying:
x = 300

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

So, 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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