The average salary of male employees in a firm was RS. 520 and that of females was Rs. 420. The mean salary of all the employees was Rs. 500. The percentage of male and female employees are

Options

A. 30, 70
B. 80, 20
C. 40, 60
D. 50, 50

Answer

To find the percentage of male and female employees in the firm based on their average salaries, we can set up the problem as follows:

### Step 1: Define Variables
Let:
- \( x \) = percentage of male employees
- \( 100 - x \) = percentage of female employees

### Step 2: Set Up the Equation
We know the average salaries:
- Average salary of male employees = Rs. 520
- Average salary of female employees = Rs. 420
- Mean salary of all employees = Rs. 500

Using the formula for the mean salary:
\[ \text{Mean Salary} = \frac{(\text{Average Salary of Males} \times \text{Percentage of Males}) + (\text{Average Salary of Females} \times \text{Percentage of Females})}{100} \]

Substituting the known values:
\[ 500 = \frac{(520 \times x) + (420 \times (100 - x))}{100} \]

### Step 3: Multiply Through by 100
To eliminate the denominator, multiply both sides by 100:
\[ 50000 = 520x + 420(100 - x) \]

### Step 4: Expand and Simplify
Now, expand the equation:
\[ 50000 = 520x + 42000 - 420x \]
Combine like terms:
\[ 50000 = 100x + 42000 \]

### Step 5: Isolate \( x \)
Subtract 42000 from both sides:
\[ 50000 - 42000 = 100x \]
\[ 8000 = 100x \]
Now, divide by 100:
\[ x = 80 \]

### Step 6: Calculate Percentage of Female Employees
Now, calculate the percentage of female employees:
\[ \text{Percentage of Female Employees} = 100 - x = 100 - 80 = 20 \]

### Conclusion
Thus, the percentage of male employees is 80% and the percentage of female employees is 20%.

### Final Answer
The percentage of male and female employees is 80% and 20%, respectively.

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