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A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?
- a)6.5 minutes
- b)7.5 minutes
- c)8.5 minutes
- d)9.5 minutes
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A large cistern can be filled by two pipes P and Q in 15 minutes and 1...
Part filled by P and Q = 1/15 + 1/10 = 1/6
Part filled by Q = 1/10
x/2(1/6 + 1/10) = 2/15 = 15/2 = 7.5 minutes
Part filled by Q = 1/10
x/2(1/6 + 1/10) = 2/15 = 15/2 = 7.5 minutes
Most Upvoted Answer
A large cistern can be filled by two pipes P and Q in 15 minutes and 1...
To solve this problem, we can use the concept of work. The work done by a pipe is equal to the product of its rate and the time it takes to fill the cistern.
Let's assume that the capacity of the cistern is 1 unit (you can assume any value as it will not affect the final answer).
The rate of pipe P is 1/15 units per minute, and the rate of pipe Q is 1/10 units per minute.
Let's break down the problem into two parts:
1. Q is used for half the time:
Since Q is used for half the time, it will fill the cistern for 1/2 * t minutes, where t is the total time taken to fill the cistern.
The work done by Q in 1/2 * t minutes is (1/2 * t) * (1/10) = t/20 units.
2. P and Q fill it together for the other half:
Since P and Q fill the cistern together for the other half of the time, they will fill the cistern for 1/2 * t minutes.
The combined rate of P and Q is (1/15) + (1/10) = 5/30 + 3/30 = 8/30 units per minute.
The work done by P and Q together in 1/2 * t minutes is (1/2 * t) * (8/30) = 4t/60 = t/15 units.
Now, we can set up an equation to find the total work done:
t/20 + t/15 = 1
Multiplying through by 60 to clear the fractions, we get:
3t + 4t = 60
7t = 60
t = 60/7
So, it will take approximately 8.57 minutes to fill the cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half.
Since the options given are in minutes, we round off the answer to the nearest minute, which is 9 minutes.
Therefore, the correct answer is option B) 7.5 minutes.
Let's assume that the capacity of the cistern is 1 unit (you can assume any value as it will not affect the final answer).
The rate of pipe P is 1/15 units per minute, and the rate of pipe Q is 1/10 units per minute.
Let's break down the problem into two parts:
1. Q is used for half the time:
Since Q is used for half the time, it will fill the cistern for 1/2 * t minutes, where t is the total time taken to fill the cistern.
The work done by Q in 1/2 * t minutes is (1/2 * t) * (1/10) = t/20 units.
2. P and Q fill it together for the other half:
Since P and Q fill the cistern together for the other half of the time, they will fill the cistern for 1/2 * t minutes.
The combined rate of P and Q is (1/15) + (1/10) = 5/30 + 3/30 = 8/30 units per minute.
The work done by P and Q together in 1/2 * t minutes is (1/2 * t) * (8/30) = 4t/60 = t/15 units.
Now, we can set up an equation to find the total work done:
t/20 + t/15 = 1
Multiplying through by 60 to clear the fractions, we get:
3t + 4t = 60
7t = 60
t = 60/7
So, it will take approximately 8.57 minutes to fill the cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half.
Since the options given are in minutes, we round off the answer to the nearest minute, which is 9 minutes.
Therefore, the correct answer is option B) 7.5 minutes.
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A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?a)6.5 minutesb)7.5 minutesc)8.5 minutesd)9.5 minutese)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?a)6.5 minutesb)7.5 minutesc)8.5 minutesd)9.5 minutese)None of the AboveCorrect answer is option 'B'. 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 A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?a)6.5 minutesb)7.5 minutesc)8.5 minutesd)9.5 minutese)None of the AboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?a)6.5 minutesb)7.5 minutesc)8.5 minutesd)9.5 minutese)None of the AboveCorrect answer is option 'B'. Can you explain this answer?.
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