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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
- a)60 gallons
- b)100 gallons
- c)120 gallons
- d)180 gallons
Correct answer is option 'C'. Can you explain this answer?
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Two pipes can fill a tank in 20 and 24 minutes respectively and a wast...
Let's assume the capacity of the tank is 'x' gallons.
The first pipe can fill the tank in 20 minutes, so its rate of filling is x/20 gallons per minute.
Similarly, the second pipe can fill the tank in 24 minutes, so its rate of filling is x/24 gallons per minute.
The waste pipe can empty 3 gallons per minute, so its rate of emptying is 3 gallons per minute.
When all three pipes are working together, they can fill the tank in 15 minutes. Let's calculate the combined rate of filling when all three pipes are working together.
Let the combined rate of filling be R gallons per minute.
According to the given information, the first pipe fills at a rate of x/20 gallons per minute, the second pipe fills at a rate of x/24 gallons per minute, and the waste pipe empties at a rate of 3 gallons per minute.
So, we can write the equation: x/20 + x/24 - 3 = R
To find the combined rate of filling, we need to find the common denominator of 20 and 24, which is 120.
Multiplying the equation by 120, we get: 6x + 5x - 360 = 120R
Simplifying the equation, we have: 11x - 360 = 120R
Now, we know that the combined rate of filling is x/15 gallons per minute since the tank is filled in 15 minutes.
So, we can write another equation: x/15 = R
Now we have two equations:
1) 11x - 360 = 120R
2) x/15 = R
We can solve these equations simultaneously to find the value of x.
Simplifying the second equation, we get: x = 15R
Substituting this value of x in the first equation, we have: 11(15R) - 360 = 120R
Simplifying the equation, we get: 165R - 360 = 120R
Bringing the variables to one side, we have: 165R - 120R = 360
Simplifying further, we get: 45R = 360
Dividing both sides by 45, we get: R = 8
Now, substituting the value of R in the equation x/15 = R, we have: x/15 = 8
Multiplying both sides by 15, we get: x = 120
Therefore, the capacity of the tank is 120 gallons, which corresponds to option 'C'.
The first pipe can fill the tank in 20 minutes, so its rate of filling is x/20 gallons per minute.
Similarly, the second pipe can fill the tank in 24 minutes, so its rate of filling is x/24 gallons per minute.
The waste pipe can empty 3 gallons per minute, so its rate of emptying is 3 gallons per minute.
When all three pipes are working together, they can fill the tank in 15 minutes. Let's calculate the combined rate of filling when all three pipes are working together.
Let the combined rate of filling be R gallons per minute.
According to the given information, the first pipe fills at a rate of x/20 gallons per minute, the second pipe fills at a rate of x/24 gallons per minute, and the waste pipe empties at a rate of 3 gallons per minute.
So, we can write the equation: x/20 + x/24 - 3 = R
To find the combined rate of filling, we need to find the common denominator of 20 and 24, which is 120.
Multiplying the equation by 120, we get: 6x + 5x - 360 = 120R
Simplifying the equation, we have: 11x - 360 = 120R
Now, we know that the combined rate of filling is x/15 gallons per minute since the tank is filled in 15 minutes.
So, we can write another equation: x/15 = R
Now we have two equations:
1) 11x - 360 = 120R
2) x/15 = R
We can solve these equations simultaneously to find the value of x.
Simplifying the second equation, we get: x = 15R
Substituting this value of x in the first equation, we have: 11(15R) - 360 = 120R
Simplifying the equation, we get: 165R - 360 = 120R
Bringing the variables to one side, we have: 165R - 120R = 360
Simplifying further, we get: 45R = 360
Dividing both sides by 45, we get: R = 8
Now, substituting the value of R in the equation x/15 = R, we have: x/15 = 8
Multiplying both sides by 15, we get: x = 120
Therefore, the capacity of the tank is 120 gallons, which corresponds to option 'C'.
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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer?
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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer?.
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer?.
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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:a)60 gallonsb)100 gallonsc)120 gallonsd)180 gallonsCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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