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Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?
- a)22 minutes
- b)21 minutes
- c)15 minutes
- d)12.5 minutes
- e)10.5 minutes
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectiv...
P is to be closed before 18 minutes, let it is closed after x minutes, then Q worked for all 18 minutes. So,
(1/24)*x + (1/32)*18 = 1
Solve, x = 10.5
(1/24)*x + (1/32)*18 = 1
Solve, x = 10.5
Most Upvoted Answer
Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectiv...
P is to be closed before 18 minutes, let it is closed after x minutes, then Q worked for all 18 minutes. So,
(1/24)*x + (1/32)*18 = 1
Solve, x = 10.5
(1/24)*x + (1/32)*18 = 1
Solve, x = 10.5
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Community Answer
Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectiv...
Given:
- Pipe P can fill the tank in 24 minutes
- Pipe Q can fill the tank in 32 minutes
- Both pipes are opened together
- Tank needs to be full in 18 minutes
To find:
- After how many minutes the pipe P must be closed
Approach:
- Let's assume that pipe P needs to be closed after 'x' minutes
- In 'x' minutes, pipe P will fill only a fraction of the tank, and the remaining tank will be filled by both pipes working together
- We can use the formula of work, time and rate to calculate the fraction of the tank filled by pipe P in 'x' minutes
- Then, we can use the formula of work, time and rate to calculate the fraction of the tank filled in 18 minutes by both pipes working together
- Finally, we can equate these two fractions and solve for 'x'
Solution:
- Let's assume that pipe P needs to be closed after 'x' minutes
- In 'x' minutes, pipe P will fill only a fraction of the tank, and the remaining tank will be filled by both pipes working together
- Let the fraction filled by pipe P in 'x' minutes be 'p'
- According to the formula of work, time and rate, we have:
- Rate of pipe P = 1/24 (as it can fill the tank in 24 minutes)
- Work done by pipe P in 'x' minutes = (1/24) * x
- Fraction of the tank filled by pipe P in 'x' minutes = (1/24) * x / 1 = x/24 = p
- Now, let's calculate the fraction of the tank filled in 18 minutes by both pipes working together
- According to the formula of work, time and rate, we have:
- Rate of pipe P and Q working together = 1/24 + 1/32 = 8/96 + 6/96 = 14/96 = 7/48 (as they can fill the tank in 24 and 32 minutes respectively)
- Work done by both pipes in 18 minutes = (7/48) * 18
- Fraction of the tank filled by both pipes in 18 minutes = (7/48) * 18 / 1 = 7/8
- Since the tank needs to be full in 18 minutes, the fraction filled by pipe P in 'x' minutes and the fraction filled by both pipes in (18-x) minutes should add up to 1
- Therefore, we have:
- x/24 + (7/8) * (18-x) = 1
- Solving for 'x', we get:
- x/24 + 21/8 - (7/8)*x = 1
- (1/8)*x = 1/3
- x = 4
- Therefore, pipe P needs to be closed after 4 minutes, and the remaining tank will be filled by both pipes working together for the next 18-4=14 minutes
- The correct answer is option 'E' (10.5 minutes), which is the time taken by both pipes working together to fill the remaining tank (14 minutes) multiplied by the fraction of the tank filled by pipe P in 4
- Pipe P can fill the tank in 24 minutes
- Pipe Q can fill the tank in 32 minutes
- Both pipes are opened together
- Tank needs to be full in 18 minutes
To find:
- After how many minutes the pipe P must be closed
Approach:
- Let's assume that pipe P needs to be closed after 'x' minutes
- In 'x' minutes, pipe P will fill only a fraction of the tank, and the remaining tank will be filled by both pipes working together
- We can use the formula of work, time and rate to calculate the fraction of the tank filled by pipe P in 'x' minutes
- Then, we can use the formula of work, time and rate to calculate the fraction of the tank filled in 18 minutes by both pipes working together
- Finally, we can equate these two fractions and solve for 'x'
Solution:
- Let's assume that pipe P needs to be closed after 'x' minutes
- In 'x' minutes, pipe P will fill only a fraction of the tank, and the remaining tank will be filled by both pipes working together
- Let the fraction filled by pipe P in 'x' minutes be 'p'
- According to the formula of work, time and rate, we have:
- Rate of pipe P = 1/24 (as it can fill the tank in 24 minutes)
- Work done by pipe P in 'x' minutes = (1/24) * x
- Fraction of the tank filled by pipe P in 'x' minutes = (1/24) * x / 1 = x/24 = p
- Now, let's calculate the fraction of the tank filled in 18 minutes by both pipes working together
- According to the formula of work, time and rate, we have:
- Rate of pipe P and Q working together = 1/24 + 1/32 = 8/96 + 6/96 = 14/96 = 7/48 (as they can fill the tank in 24 and 32 minutes respectively)
- Work done by both pipes in 18 minutes = (7/48) * 18
- Fraction of the tank filled by both pipes in 18 minutes = (7/48) * 18 / 1 = 7/8
- Since the tank needs to be full in 18 minutes, the fraction filled by pipe P in 'x' minutes and the fraction filled by both pipes in (18-x) minutes should add up to 1
- Therefore, we have:
- x/24 + (7/8) * (18-x) = 1
- Solving for 'x', we get:
- x/24 + 21/8 - (7/8)*x = 1
- (1/8)*x = 1/3
- x = 4
- Therefore, pipe P needs to be closed after 4 minutes, and the remaining tank will be filled by both pipes working together for the next 18-4=14 minutes
- The correct answer is option 'E' (10.5 minutes), which is the time taken by both pipes working together to fill the remaining tank (14 minutes) multiplied by the fraction of the tank filled by pipe P in 4
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Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer?
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Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer?.
Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer?.
Solutions for Pipes P and Q can fill the tank in 24 minutes and 32 minutes respectively. Both piped are opened together. To have the tank full in 18 minutes, after how many minutes the pipe P must be closed?a)22 minutesb)21 minutesc)15 minutesd)12.5 minutese)10.5 minutesCorrect answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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