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In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.
- a)10.5 minutes
- b)11.5 minutes
- c)12.5 minutes
- d)13.5 minutes
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In what time would a cistern be filled by three pipes whose diameters ...
More the diameter more will be the water flowing through it and less will be the time taken.
Means bigger pipe will take less time to fill the tank
So, for 1 cm time, (12)/(32) = 21/t, we get t = 189
For 2 cm time, (22)/(32) = 21/t. We get t = 189/4
So total time = 1/21 + 1/189 + 4/189 = 2/27
So total time = 13.5 minutes
Means bigger pipe will take less time to fill the tank
So, for 1 cm time, (12)/(32) = 21/t, we get t = 189
For 2 cm time, (22)/(32) = 21/t. We get t = 189/4
So total time = 1/21 + 1/189 + 4/189 = 2/27
So total time = 13.5 minutes
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In what time would a cistern be filled by three pipes whose diameters ...
Given information:
- The largest pipe alone can fill the tank in 21 minutes.
- The amount of water flowing through the pipe is directly proportional to the square of its diameter.
To find the time taken by three pipes to fill the cistern together, we need to consider the rate of water flow through each pipe. Let's denote the rates as R1, R2, and R3 for the pipes with diameters 1cm, 2cm, and 3cm respectively.
Since the amount of water flowing through the pipe is directly proportional to the square of its diameter, we can write the equation:
R1 : R2 : R3 = (1cm)^2 : (2cm)^2 : (3cm)^2 = 1 : 4 : 9
Let's assume the time taken by the three pipes to fill the cistern together is T minutes.
Calculation:
- The largest pipe alone can fill the cistern in 21 minutes, so its rate of water flow is 1/21 of the cistern per minute.
- The rate of the second pipe (R2) is 4 times that of the first pipe, so it can fill the cistern at a rate of 4/21 of the cistern per minute.
- Similarly, the rate of the third pipe (R3) is 9 times that of the first pipe, so it can fill the cistern at a rate of 9/21 = 3/7 of the cistern per minute.
Now, let's add up the rates of the three pipes working together:
R1 + R2 + R3 = 1/21 + 4/21 + 3/7 = 1/21 + 8/21 + 9/21 = 18/21 = 6/7 of the cistern per minute.
Since the combined rate of the three pipes is 6/7 of the cistern per minute, we can set up the equation:
(6/7) * T = 1 (as they fill the cistern together)
Solving for T:
T = 7/6 minutes = 1.1667 minutes
Converting the time to minutes and seconds:
T = 1 minute + 0.1667 * 60 seconds = 1 minute + 10 seconds = 1 minute 10 seconds
Therefore, the time taken by the three pipes to fill the cistern together is approximately 1 minute and 10 seconds, which is equivalent to 1.1667 minutes.
Rounded to the nearest minute, the answer is 1 minute.
- The largest pipe alone can fill the tank in 21 minutes.
- The amount of water flowing through the pipe is directly proportional to the square of its diameter.
To find the time taken by three pipes to fill the cistern together, we need to consider the rate of water flow through each pipe. Let's denote the rates as R1, R2, and R3 for the pipes with diameters 1cm, 2cm, and 3cm respectively.
Since the amount of water flowing through the pipe is directly proportional to the square of its diameter, we can write the equation:
R1 : R2 : R3 = (1cm)^2 : (2cm)^2 : (3cm)^2 = 1 : 4 : 9
Let's assume the time taken by the three pipes to fill the cistern together is T minutes.
Calculation:
- The largest pipe alone can fill the cistern in 21 minutes, so its rate of water flow is 1/21 of the cistern per minute.
- The rate of the second pipe (R2) is 4 times that of the first pipe, so it can fill the cistern at a rate of 4/21 of the cistern per minute.
- Similarly, the rate of the third pipe (R3) is 9 times that of the first pipe, so it can fill the cistern at a rate of 9/21 = 3/7 of the cistern per minute.
Now, let's add up the rates of the three pipes working together:
R1 + R2 + R3 = 1/21 + 4/21 + 3/7 = 1/21 + 8/21 + 9/21 = 18/21 = 6/7 of the cistern per minute.
Since the combined rate of the three pipes is 6/7 of the cistern per minute, we can set up the equation:
(6/7) * T = 1 (as they fill the cistern together)
Solving for T:
T = 7/6 minutes = 1.1667 minutes
Converting the time to minutes and seconds:
T = 1 minute + 0.1667 * 60 seconds = 1 minute + 10 seconds = 1 minute 10 seconds
Therefore, the time taken by the three pipes to fill the cistern together is approximately 1 minute and 10 seconds, which is equivalent to 1.1667 minutes.
Rounded to the nearest minute, the answer is 1 minute.
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In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?.
In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.a)10.5 minutesb)11.5 minutesc)12.5 minutesd)13.5 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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