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Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?
- a)90 min
- b)100 min
- c)110 min
- d)120 min
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted 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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Two pipes A and B can separately fill a cistern in 60 minutes and 75 m...
Given:
Pipe A fills the cistern in 60 minutes.
Pipe B fills the cistern in 75 minutes.
All three pipes together fill the cistern in 50 minutes.
To find:
The time taken by the third pipe alone to empty the cistern.
Approach:
Let's assume the capacity of the cistern is C liters.
Let the rate of filling of pipe A be R liters/minute.
Let the rate of filling of pipe B be S liters/minute.
Let the rate of emptying of the third pipe be T liters/minute.
From the given information, we can calculate the following:
Rate of filling of pipe A, R = C/60 liters/minute
Rate of filling of pipe B, S = C/75 liters/minute
Now, let's consider the scenario where all three pipes are opened together:
Rate of filling of all three pipes combined = Rate of filling of pipe A + Rate of filling of pipe B - Rate of emptying of the third pipe
Rate of filling of all three pipes combined = R + S - T liters/minute
Given that the cistern is filled in 50 minutes when all three pipes are opened together, we have:
50 * (R + S - T) = C
We also know that the time taken by the third pipe alone to empty the cistern is given by:
T = C/T
Simplifying the equation, we get:
50R + 50S - 50T = C
Since R = C/60 and S = C/75, we can substitute these values in the equation:
50(C/60) + 50(C/75) - 50T = C
Simplifying further, we get:
5C + 4C - 5T = 6C
Rearranging the equation, we get:
6C - 9C = 5T
Simplifying, we get:
-3C = 5T
Dividing both sides by -3, we get:
C = -5T/3
Since the capacity of the cistern cannot be negative, we can ignore the negative sign.
So, C = 5T/3
Substituting the value of C in the equation 50(R + S - T) = C, we get:
50(R + S - T) = 5T/3
Simplifying further, we get:
10(R + S - T) = T
Expanding, we get:
10R + 10S - 10T = T
Rearranging the equation, we get:
10T + 10T = 10R + 10S
Simplifying, we get:
20T = 10R + 10S
Dividing both sides by 10, we get:
2T = R + S
Substituting the values of R and S, we get:
2T = C/60 + C/75
Finding the common denominator, we get:
2T = (5C + 4C)/300
Simplifying the equation, we get:
2T = 9C/300
Dividing both sides by 2, we get:
T = 9C/600
Simplifying further, we get:
T = C/66.67
Since the time taken by the third
Pipe A fills the cistern in 60 minutes.
Pipe B fills the cistern in 75 minutes.
All three pipes together fill the cistern in 50 minutes.
To find:
The time taken by the third pipe alone to empty the cistern.
Approach:
Let's assume the capacity of the cistern is C liters.
Let the rate of filling of pipe A be R liters/minute.
Let the rate of filling of pipe B be S liters/minute.
Let the rate of emptying of the third pipe be T liters/minute.
From the given information, we can calculate the following:
Rate of filling of pipe A, R = C/60 liters/minute
Rate of filling of pipe B, S = C/75 liters/minute
Now, let's consider the scenario where all three pipes are opened together:
Rate of filling of all three pipes combined = Rate of filling of pipe A + Rate of filling of pipe B - Rate of emptying of the third pipe
Rate of filling of all three pipes combined = R + S - T liters/minute
Given that the cistern is filled in 50 minutes when all three pipes are opened together, we have:
50 * (R + S - T) = C
We also know that the time taken by the third pipe alone to empty the cistern is given by:
T = C/T
Simplifying the equation, we get:
50R + 50S - 50T = C
Since R = C/60 and S = C/75, we can substitute these values in the equation:
50(C/60) + 50(C/75) - 50T = C
Simplifying further, we get:
5C + 4C - 5T = 6C
Rearranging the equation, we get:
6C - 9C = 5T
Simplifying, we get:
-3C = 5T
Dividing both sides by -3, we get:
C = -5T/3
Since the capacity of the cistern cannot be negative, we can ignore the negative sign.
So, C = 5T/3
Substituting the value of C in the equation 50(R + S - T) = C, we get:
50(R + S - T) = 5T/3
Simplifying further, we get:
10(R + S - T) = T
Expanding, we get:
10R + 10S - 10T = T
Rearranging the equation, we get:
10T + 10T = 10R + 10S
Simplifying, we get:
20T = 10R + 10S
Dividing both sides by 10, we get:
2T = R + S
Substituting the values of R and S, we get:
2T = C/60 + C/75
Finding the common denominator, we get:
2T = (5C + 4C)/300
Simplifying the equation, we get:
2T = 9C/300
Dividing both sides by 2, we get:
T = 9C/600
Simplifying further, we get:
T = C/66.67
Since the time taken by the third
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Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect 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 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 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 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Two pipes A and B can separately fill a cistern in 60 minutes and 75 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 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 minutes respectively. There is a third pipe in 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, the third pipe alone can empty the cistern?a)90 minb)100 minc)110 mind)120 mine)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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