The average income of male employees in a financial sector company A was Rs 520 and that of females was Rs 420. The mean income of all the employees was Rs 500. The percentage of male employees is

Options

A. `50%`
B. `80%`
C. `40%`
D. `20%`

Answer

To find the percentage of male employees in the company based on the given average incomes, we can follow these steps:

### Step 1: Define Variables
Let:
- \( M \) = number of male employees
- \( F \) = number of female employees
- \( A_m \) = average income of male employees = Rs 520
- \( A_f \) = average income of female employees = Rs 420
- \( A \) = average income of all employees = Rs 500

### Step 2: Set Up the Equation for Average Income
The formula for the average income of all employees is given by:
\[ A = \frac{M \cdot A_m + F \cdot A_f}{M + F} \]
Substituting the known values:
\[ 500 = \frac{M \cdot 520 + F \cdot 420}{M + F} \]

### Step 3: Rearranging the Equation
Multiply both sides by \( M + F \):
\[ 500(M + F) = 520M + 420F \]
Expanding this gives:
\[ 500M + 500F = 520M + 420F \]

### Step 4: Simplifying the Equation
Rearranging the terms:
\[ 500M + 500F - 520M - 420F = 0 \]
This simplifies to:
\[ -20M + 80F = 0 \]
Or:
\[ 20M = 80F \]
Dividing both sides by 20:
\[ M = 4F \]

### Step 5: Finding the Total Number of Employees
Now, we can express the total number of employees \( N \) in terms of \( F \):
\[ N = M + F = 4F + F = 5F \]

### Step 6: Calculating the Percentage of Male Employees
The percentage of male employees is given by:
\[ \text{Percentage of Male Employees} = \left(\frac{M}{N}\right) \times 100 \]
Substituting \( M \) and \( N \):
\[ \text{Percentage of Male Employees} = \left(\frac{4F}{5F}\right) \times 100 = \frac{4}{5} \times 100 = 80\% \]

### Final Answer
The percentage of male employees in the company is **80%**.

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