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In what time would a cistern be filled by three pipes of diameter of 1 cm, 2 cm and 3 cm if the largest pipe alone can fill the cistern in 49 minutes, the amount of water flowing through each pipe being proportional to the square of its diameter?
- a)31.5 minutes
- b)63 minutes
- c)126 minutes
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In what time would a cistern be filled by three pipes of diameter of 1...
Since the amount of water flowing through each pipe is proportional to the square of its diameter , if efficiency of longest pipe (3 cm) = 1/49
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Then efficiency of pipe (2 cm) = 4 / (49 x 9)
and efficiency of pipe (1 cm) = 1 / (49 x 9)
Now , let the cistern is filled by all the three pipes in x minutes.
So , 1 / 49 + 4 / 49 x 9 + 1 / 49 x 9 = 1 / x
= x = 31.5 minutes.
Most Upvoted Answer
In what time would a cistern be filled by three pipes of diameter of 1...
Answer a. 31.5 minutes
efficiency by squaring diameters 1, 4, 9 units. hence 49*9 is 441 units.
1+4+9 is 14 units per unit. so 31.5 minutes to fill full capacity
efficiency by squaring diameters 1, 4, 9 units. hence 49*9 is 441 units.
1+4+9 is 14 units per unit. so 31.5 minutes to fill full capacity
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In what time would a cistern be filled by three pipes of diameter of 1...
Given:
- Diameter of first pipe = 1 cm
- Diameter of second pipe = 2 cm
- Diameter of third pipe = 3 cm
- Time taken by largest pipe to fill the cistern alone = 49 minutes
To find:
- Time taken by all three pipes together to fill the cistern
Approach:
- Let the amount of water flowing through the largest pipe be x units per minute
- Then, amount of water flowing through first pipe = (1/3)^2 * x = x/9 units per minute
- Amount of water flowing through second pipe = (2/3)^2 * x = 4x/9 units per minute
- Amount of water flowing through third pipe = x units per minute
- Let the time taken by all three pipes together to fill the cistern be t minutes
- Then, using the concept of work, we can set up an equation as follows:
- Work done by largest pipe in t minutes + Work done by first pipe in t minutes + Work done by second pipe in t minutes + Work done by third pipe in t minutes = 1 (i.e., filling the cistern completely)
- x * t + (x/9) * t + (4x/9) * t + x * t = 1
- Simplifying, we get: t = 9/31.5
Therefore, the time taken by all three pipes together to fill the cistern is 9/31.5 minutes, which is approximately equal to 31.5 minutes. Hence, the correct option is (a) 31.5 minutes.
- Diameter of first pipe = 1 cm
- Diameter of second pipe = 2 cm
- Diameter of third pipe = 3 cm
- Time taken by largest pipe to fill the cistern alone = 49 minutes
To find:
- Time taken by all three pipes together to fill the cistern
Approach:
- Let the amount of water flowing through the largest pipe be x units per minute
- Then, amount of water flowing through first pipe = (1/3)^2 * x = x/9 units per minute
- Amount of water flowing through second pipe = (2/3)^2 * x = 4x/9 units per minute
- Amount of water flowing through third pipe = x units per minute
- Let the time taken by all three pipes together to fill the cistern be t minutes
- Then, using the concept of work, we can set up an equation as follows:
- Work done by largest pipe in t minutes + Work done by first pipe in t minutes + Work done by second pipe in t minutes + Work done by third pipe in t minutes = 1 (i.e., filling the cistern completely)
- x * t + (x/9) * t + (4x/9) * t + x * t = 1
- Simplifying, we get: t = 9/31.5
Therefore, the time taken by all three pipes together to fill the cistern is 9/31.5 minutes, which is approximately equal to 31.5 minutes. Hence, the correct option is (a) 31.5 minutes.
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In what time would a cistern be filled by three pipes of diameter of 1 cm, 2 cm and 3 cm if the largest pipe alone can fill the cistern in 49 minutes, the amount of water flowing through each pipe being proportional to the square of its diameter?a)31.5 minutesb)63 minutesc)126 minutesd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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