If the harmonic mean of 60 and x is 48, then what is the value of x ?

Options

A. 32
B. 36
C. 40
D. 44

Answer

To find the value of \( x \) given that the harmonic mean of 60 and \( x \) is 48, we can follow these steps:

### Step 1: Understand the formula for Harmonic Mean
The harmonic mean \( H \) of two numbers \( A \) and \( B \) is given by the formula:
\[ H = \frac{2AB}{A + B} \]
where \( A \) and \( B \) are the two numbers.

### Step 2: Assign values to the variables
In this case, we have:
- \( A = 60 \)
- \( B = x \)
- \( H = 48 \)

### Step 3: Substitute the values into the formula
Using the formula for harmonic mean, we can substitute the values:
\[ 48 = \frac{2 \cdot 60 \cdot x}{60 + x} \]

### Step 4: Simplify the equation
Multiply both sides by \( (60 + x) \) to eliminate the denominator:
\[ 48(60 + x) = 120x \]

### Step 5: Expand the left side
Distributing \( 48 \) on the left side gives:
\[ 2880 + 48x = 120x \]

### Step 6: Rearrange the equation
Now, we will move \( 48x \) to the right side:
\[ 2880 = 120x - 48x \]
This simplifies to:
\[ 2880 = 72x \]

### Step 7: Solve for \( x \)
Now, divide both sides by 72 to find \( x \):
\[ x = \frac{2880}{72} \]

### Step 8: Calculate the value
Now, perform the division:
\[ x = 40 \]

Thus, the value of \( x \) is \( 40 \).