The average salary of male employee in a firm was Rs. 5200 and that of female was Rs. 4200. The average salary of all the employees was Rs. 5000.What is the percentage of female employees?

Options

A. `80%`
B. `20%`
C. `40%`
D. `30%`

Answer

To solve the problem step by step, we will denote the number of male employees as \( X \) and the number of female employees as \( Y \).

### Step 1: Set up the equations based on the given averages.
- The average salary of male employees is Rs. 5200.
- The average salary of female employees is Rs. 4200.
- The average salary of all employees is Rs. 5000.

From this information, we can express the total salaries:
- Total salary of male employees = \( 5200X \)
- Total salary of female employees = \( 4200Y \)
- Total salary of all employees = \( 5000(X + Y) \)

### Step 2: Write the equation for total salaries.
We can set up the equation based on the total salaries:
\[ 5200X + 4200Y = 5000(X + Y) \]

### Step 3: Expand and simplify the equation.
Expanding the right side:
\[ 5200X + 4200Y = 5000X + 5000Y \]

Now, rearranging the equation:
\[ 5200X + 4200Y - 5000X - 5000Y = 0 \]
\[ (5200 - 5000)X + (4200 - 5000)Y = 0 \]
\[ 200X - 800Y = 0 \]

### Step 4: Simplify the equation.
Dividing the entire equation by 200:
\[ X - 4Y = 0 \]
This implies:
\[ X = 4Y \]

### Step 5: Find the ratio of male to female employees.
From the equation \( X = 4Y \), we can express the ratio of male to female employees:
\[ \frac{X}{Y} = \frac{4}{1} \]

### Step 6: Calculate the total number of employees.
The total number of employees is:
\[ X + Y = 4Y + Y = 5Y \]

### Step 7: Calculate the percentage of female employees.
The percentage of female employees is given by:
\[ \text{Percentage of female employees} = \left( \frac{Y}{X + Y} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of female employees} = \left( \frac{Y}{5Y} \right) \times 100 = \left( \frac{1}{5} \right) \times 100 = 20\% \]

### Final Answer:
The percentage of female employees in the firm is **20%**.

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