In a company, the average salary of male employees is Rs `8200` and that of female employees is Rs `7200`. If the average salary per employee is Rs `7900`, then the percentage of female employees of the total employees is________

Options

A. `30 %`
B. `40 %`
C. `50 %`
D. `25 %`

Answer

To solve the problem step-by-step, we will use the information provided about the average salaries of male and female employees, as well as the overall average salary.

### Step 1: Define Variables
Let:
- \( X \) = Number of male employees
- \( Y \) = Number of female employees

### Step 2: Write the Total Salaries
The total salary of male employees can be expressed as:
- Total salary of males = \( 8200 \times X \)

The total salary of female employees can be expressed as:
- Total salary of females = \( 7200 \times Y \)

### Step 3: Write the Equation for Average Salary
The average salary per employee is given as Rs. 7900. Therefore, the total salary of all employees can also be expressed as:
- Total salary of all employees = \( 7900 \times (X + Y) \)

### Step 4: Set Up the Equation
According to the information, the total salary of all employees (sum of male and female salaries) must equal the average salary multiplied by the total number of employees:
\[ 7900 \times (X + Y) = 8200 \times X + 7200 \times Y \]

### Step 5: Expand and Rearrange the Equation
Expanding the left side:
\[ 7900X + 7900Y = 8200X + 7200Y \]

Now, rearranging the equation:
\[ 7900Y - 7200Y = 8200X - 7900X \]
This simplifies to:
\[ 700Y = 300X \]

### Step 6: Simplify the Ratio
Dividing both sides by 100:
\[ 7Y = 3X \]

### Step 7: Express the Ratio of Male to Female Employees
Rearranging gives:
\[ \frac{X}{Y} = \frac{7}{3} \]

### Step 8: Express in Terms of a Common Variable
Let \( X = 7k \) and \( Y = 3k \) for some integer \( k \).

### Step 9: Find Total Employees
The total number of employees \( T \) is:
\[ T = X + Y = 7k + 3k = 10k \]

### Step 10: Calculate the Percentage of Female Employees
The percentage of female employees is given by:
\[ \text{Percentage of female employees} = \left( \frac{Y}{T} \right) \times 100 = \left( \frac{3k}{10k} \right) \times 100 \]
This simplifies to:
\[ \text{Percentage of female employees} = \frac{3}{10} \times 100 = 30\% \]

### Final Answer
The percentage of female employees of the total employees is **30%**.

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