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The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?
- a)16.2
- b)17.3
- c)18
- d)20
Correct answer is option 'C'. Can you explain this answer?
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The harmonic mean of two numbers is 21.6. If one of the numbers is 27,...
Harmonic Mean
The harmonic mean is a mathematical concept used to calculate the average of a set of numbers. It is defined as the reciprocal of the arithmetic mean of the reciprocals of the given numbers. In other words, for two numbers a and b, the harmonic mean is given by:
Harmonic Mean = 2 / (1/a + 1/b) = 2ab / (a + b)
Solution
Let's use the given information to find the other number.
Step 1: Write the given information
The harmonic mean of two numbers is 21.6.
One of the numbers is 27.
Step 2: Substitute the given values into the formula
Using the formula for harmonic mean, we can write:
21.6 = 2 * 27 * b / (27 + b)
Step 3: Solve for the other number
To find the other number, we need to solve the equation for b.
Multiplying both sides of the equation by (27 + b), we get:
21.6 * (27 + b) = 2 * 27 * b
583.2 + 21.6b = 54b
583.2 = 54b - 21.6b
583.2 = 32.4b
Dividing both sides of the equation by 32.4, we get:
b = 583.2 / 32.4
b = 18
Therefore, the other number is 18.
Conclusion
The other number is 18. Hence, the correct answer is option C) 18.
The harmonic mean is a mathematical concept used to calculate the average of a set of numbers. It is defined as the reciprocal of the arithmetic mean of the reciprocals of the given numbers. In other words, for two numbers a and b, the harmonic mean is given by:
Harmonic Mean = 2 / (1/a + 1/b) = 2ab / (a + b)
Solution
Let's use the given information to find the other number.
Step 1: Write the given information
The harmonic mean of two numbers is 21.6.
One of the numbers is 27.
Step 2: Substitute the given values into the formula
Using the formula for harmonic mean, we can write:
21.6 = 2 * 27 * b / (27 + b)
Step 3: Solve for the other number
To find the other number, we need to solve the equation for b.
Multiplying both sides of the equation by (27 + b), we get:
21.6 * (27 + b) = 2 * 27 * b
583.2 + 21.6b = 54b
583.2 = 54b - 21.6b
583.2 = 32.4b
Dividing both sides of the equation by 32.4, we get:
b = 583.2 / 32.4
b = 18
Therefore, the other number is 18.
Conclusion
The other number is 18. Hence, the correct answer is option C) 18.
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The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer?
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The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer?.
The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?a)16.2b)17.3c)18d)20Correct answer is option 'C'. Can you explain this answer?.
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