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In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?
- a)36 minutes
- b)40 minutes
- c)60 minutes
- d)25 minutes
Correct answer is option 'A'. Can you explain this answer?
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In what time a cistern be filled by three pipes whose diameters are 1...
Portion of the cistern filled by the pipe of diameter 2cm = 1/61
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Portion of the cistern filled by pipe of diameter 1cm = 1/61 X (1/2)2 = 1/61 X 1/4
Portion of the cistern filled by pipe of diameter 1(1/3cm) = 1/61 X 1/4 X (4/3)2=1/61 X 4/9
When all the three pipes are open, the portion of the cistern filled is = 1/61+1/61 X 1/4+ 1/61 X 4/9
1/61+1/61 X 1/4+ 1/61 X 4/9 = 1/36
Therefore the time taken is 36 minutes.
Most Upvoted Answer
In what time a cistern be filled by three pipes whose diameters are 1...
Given:
Diameters of pipes = 1 cm, 1(1/3) cm, 2 cm
Time taken by largest pipe alone to fill the cistern = 61 minutes
Amount of water flowing in each pipe is proportional to the square of its diameter.
To find:
Time taken by three pipes together to fill the cistern.
Solution:
Let the amount of water flowing through the pipes be W1, W2, and W3 for diameters d1, d2, and d3 respectively. Then we have:
W1 : W2 : W3 = d1^2 : d2^2 : d3^2
Let the total time taken by the three pipes to fill the cistern be t minutes. Then the amount of water filled by each pipe in t minutes is proportional to its water flow rate.
Let V be the volume of the cistern.
Then, we have:
V/d1^2 : V/d2^2 : V/d3^2 = W1 : W2 : W3
Let x be the time taken by the largest pipe (d3 = 2 cm) to fill the cistern alone (i.e., V).
Then, we have:
V/4 : V/d2^2 : V = 1 : d2^2/4 : 1
Simplifying this equation, we get:
d2^2 = 4/3
Therefore, d2 = sqrt(4/3) = 1.1547 cm (approx)
Let y be the time taken by the other two pipes (d1 = 1 cm, d2 = 1(1/3) cm) to fill the remaining volume of the cistern (i.e., V - (V/2) = V/2).
Then, we have:
V/1^2 : V/(4/3) : V/2^2 = 1 : (4/3)/(16/9) : 1
Simplifying this equation, we get:
y = 36 minutes
Therefore, the total time taken by the three pipes together to fill the cistern is:
t = x + y = 61 + 36 = 97 minutes
Hence, the correct answer is option (A) 36 minutes.
Diameters of pipes = 1 cm, 1(1/3) cm, 2 cm
Time taken by largest pipe alone to fill the cistern = 61 minutes
Amount of water flowing in each pipe is proportional to the square of its diameter.
To find:
Time taken by three pipes together to fill the cistern.
Solution:
Let the amount of water flowing through the pipes be W1, W2, and W3 for diameters d1, d2, and d3 respectively. Then we have:
W1 : W2 : W3 = d1^2 : d2^2 : d3^2
Let the total time taken by the three pipes to fill the cistern be t minutes. Then the amount of water filled by each pipe in t minutes is proportional to its water flow rate.
Let V be the volume of the cistern.
Then, we have:
V/d1^2 : V/d2^2 : V/d3^2 = W1 : W2 : W3
Let x be the time taken by the largest pipe (d3 = 2 cm) to fill the cistern alone (i.e., V).
Then, we have:
V/4 : V/d2^2 : V = 1 : d2^2/4 : 1
Simplifying this equation, we get:
d2^2 = 4/3
Therefore, d2 = sqrt(4/3) = 1.1547 cm (approx)
Let y be the time taken by the other two pipes (d1 = 1 cm, d2 = 1(1/3) cm) to fill the remaining volume of the cistern (i.e., V - (V/2) = V/2).
Then, we have:
V/1^2 : V/(4/3) : V/2^2 = 1 : (4/3)/(16/9) : 1
Simplifying this equation, we get:
y = 36 minutes
Therefore, the total time taken by the three pipes together to fill the cistern is:
t = x + y = 61 + 36 = 97 minutes
Hence, the correct answer is option (A) 36 minutes.
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In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer?
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In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer?.
In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what time a cistern be filled by three pipes whose diameters are 1cm, 1(1/3) cm, and 2 cm is running together, when the largest alone will fill it in 61 minutes. It is found that the amount of water flowing in each pipe is proportional to the square of the diameter?a)36 minutesb)40 minutesc)60 minutesd)25 minutesCorrect answer is option 'A'. Can you explain this answer?.
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