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?

Question

Answer

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.

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