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Two pipes can fill a cistern in 20 minutes and 10 minutes, respectively. Third pipe can empty it in 25 minutes. Given that 1/5th of the cistern is already full, in how much time will the cistern be full if all three pipes are opened together?
- a)100/11 minutes
- b)90/11 minutes
- c)80/11 minutes
- d)70/11 minutes
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two pipes can fill a cistern in 20 minutes and 10 minutes, respectivel...
**Problem Analysis:**
Let's assume that the capacity of the cistern is C liters.
Given:
- Pipe A can fill the cistern in 20 minutes, which means it can fill 1/20th of the cistern in 1 minute.
- Pipe B can fill the cistern in 10 minutes, which means it can fill 1/10th of the cistern in 1 minute.
- Pipe C can empty the cistern in 25 minutes, which means it can remove 1/25th of the cistern in 1 minute.
We are also given that 1/5th of the cistern is already full, which means the cistern has (1/5)C liters of water in it initially.
**Solution Approach:**
To find the time taken to fill the cistern when all three pipes are opened together, we can use the concept of relative speed of filling or emptying.
When all three pipes are opened together, the net fill rate will be the sum of the fill rates of Pipe A and Pipe B and the empty rate of Pipe C. We can calculate the net fill rate as follows:
Net fill rate = Fill rate of Pipe A + Fill rate of Pipe B - Empty rate of Pipe C
Net fill rate = 1/20 + 1/10 - 1/25
Net fill rate = (5 + 10 - 4)/100
Net fill rate = 11/100
This means that when all three pipes are opened together, the cistern will fill at a rate of 11/100th of its capacity per minute.
Now, we need to find the time taken to fill the remaining (4/5)C liters of water in the cistern.
**Calculation:**
Let's assume the time taken to fill the remaining (4/5)C liters of water is T minutes.
Fill rate * Time = Amount filled
(11/100) * T = (4/5)C
T = (4/5)C * (100/11)
T = 80C/11
Therefore, the time taken to fill the cistern when all three pipes are opened together is 80C/11 minutes.
Since the capacity of the cistern is not given, we can cancel out the 'C' term in the numerator and denominator:
T = 80/11 minutes
Hence, the correct answer is option C) 80/11 minutes.
Let's assume that the capacity of the cistern is C liters.
Given:
- Pipe A can fill the cistern in 20 minutes, which means it can fill 1/20th of the cistern in 1 minute.
- Pipe B can fill the cistern in 10 minutes, which means it can fill 1/10th of the cistern in 1 minute.
- Pipe C can empty the cistern in 25 minutes, which means it can remove 1/25th of the cistern in 1 minute.
We are also given that 1/5th of the cistern is already full, which means the cistern has (1/5)C liters of water in it initially.
**Solution Approach:**
To find the time taken to fill the cistern when all three pipes are opened together, we can use the concept of relative speed of filling or emptying.
When all three pipes are opened together, the net fill rate will be the sum of the fill rates of Pipe A and Pipe B and the empty rate of Pipe C. We can calculate the net fill rate as follows:
Net fill rate = Fill rate of Pipe A + Fill rate of Pipe B - Empty rate of Pipe C
Net fill rate = 1/20 + 1/10 - 1/25
Net fill rate = (5 + 10 - 4)/100
Net fill rate = 11/100
This means that when all three pipes are opened together, the cistern will fill at a rate of 11/100th of its capacity per minute.
Now, we need to find the time taken to fill the remaining (4/5)C liters of water in the cistern.
**Calculation:**
Let's assume the time taken to fill the remaining (4/5)C liters of water is T minutes.
Fill rate * Time = Amount filled
(11/100) * T = (4/5)C
T = (4/5)C * (100/11)
T = 80C/11
Therefore, the time taken to fill the cistern when all three pipes are opened together is 80C/11 minutes.
Since the capacity of the cistern is not given, we can cancel out the 'C' term in the numerator and denominator:
T = 80/11 minutes
Hence, the correct answer is option C) 80/11 minutes.
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Community Answer
Two pipes can fill a cistern in 20 minutes and 10 minutes, respectivel...
Two pipes can fill a cistern in 20 minutes and 10 minutes, respectively.
In one minute, pipes can fill 1/20 and 1/10 of the cistern, respectively.
Third pipe can empty it in 25 minutes.
In one minute, third pipe can empty 1/25 of the cistern.
1/5th of the cistern is already full, it means 4/5th remains empty.
In one minute, part of the cistern filled is:
In one minute, pipes can fill 1/20 and 1/10 of the cistern, respectively.
Third pipe can empty it in 25 minutes.
In one minute, third pipe can empty 1/25 of the cistern.
1/5th of the cistern is already full, it means 4/5th remains empty.
In one minute, part of the cistern filled is:
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Two pipes can fill a cistern in 20 minutes and 10 minutes, respectively. Third pipe can empty it in 25 minutes. Given that 1/5th of the cistern is already full, in how much time will the cistern be full if all three pipes are opened together?a)100/11minutesb)90/11minutesc)80/11minutesd)70/11minutesCorrect answer is option 'C'. Can you explain this answer?
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