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

Options

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

Answer

To solve the problem step by step, we will use the method of allegation to find the percentage of female employees in the firm.

### Step 1: Identify the average salaries
- Average salary of male employees = Rs. 5200
- Average salary of female employees = Rs. 4200
- Mean salary of all employees = Rs. 5000

### Step 2: Set up the allegation
We will use the allegation method to find the ratio of male to female employees. The formula for allegation is:

\[ \text{Difference between male salary and mean salary} = |5200 - 5000| = 200 \]
\[ \text{Difference between female salary and mean salary} = |4200 - 5000| = 800 \]

### Step 3: Write the allegation
Now, we can set up the allegation:
- The difference between the male salary and the mean salary is Rs. 200.
- The difference between the female salary and the mean salary is Rs. 800.

This gives us the ratio of male to female employees:
\[ \text{Ratio} = \frac{800}{200} = 4:1 \]

### Step 4: Determine the total parts
In the ratio 4:1, the total parts = 4 (male) + 1 (female) = 5 parts.

### Step 5: Calculate the percentage of female employees
To find the percentage of female employees:
\[ \text{Percentage of female employees} = \left(\frac{\text{Number of female parts}}{\text{Total parts}}\right) \times 100 = \left(\frac{1}{5}\right) \times 100 = 20\% \]

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

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