The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?

Options

A. 16.2
B. 17.3
C. 18
D. 20

Explanation

To solve the problem, we need to find the other number given that the harmonic mean of two numbers is 21.6 and one of the numbers is 27.

### Step-by-Step Solution:

1. **Understanding Harmonic Mean**: The formula for the harmonic mean (HM) of two numbers \( A \) and \( B \) is given by:
\[ HM = \frac{2AB}{A + B} \]
Here, we know that \( HM = 21.6 \) and one of the numbers \( A = 27 \). We need to find the other number \( B \).

2. **Substituting Known Values**: Substitute \( A = 27 \) into the harmonic mean formula:
\[ 21.6 = \frac{2 \times 27 \times B}{27 + B} \]

3. **Simplifying the Equation**: Multiply both sides by \( (27 + B) \) to eliminate the fraction:
\[ 21.6(27 + B) = 54B \]

4. **Expanding the Left Side**: Distributing \( 21.6 \) on the left side:
\[ 583.2 + 21.6B = 54B \]

5. **Rearranging the Equation**: Move all terms involving \( B \) to one side:
\[ 583.2 = 54B - 21.6B \]
Simplifying the right side gives:
\[ 583.2 = 32.4B \]

6. **Solving for \( B \)**: Divide both sides by \( 32.4 \) to find \( B \):
\[ B = \frac{583.2}{32.4} \]
Calculating this gives:
\[ B = 18 \]

7. **Conclusion**: The other number is \( 18 \).

### Final Answer:
The other number is **18**.