The ratio between the male and female existing employees in an organisation is 9 : 7. The ratio between the male and female in a new recruitment of 360 employees is 4 : 5. The new ratio between male and female employees after recruitment becomes 61 : 55. Find the difference between the male and female employees before recruitment?

Options

A. 80
B. 120
C. 100
D. 160

Answer

To solve the problem step by step, we will follow the given ratios and perform calculations accordingly.

### Step 1: Define the initial number of male and female employees
Let the number of male employees be \( 9x \) and the number of female employees be \( 7x \).

### Step 2: Calculate the total number of existing employees
The total number of existing employees is:
\[ 9x + 7x = 16x \]

### Step 3: Determine the number of new male and female employees from recruitment
In the new recruitment of 360 employees, the ratio of male to female is 4:5.
To find the number of male and female employees recruited, we can set up the following equations:
- Total parts = \( 4 + 5 = 9 \)
- Male employees recruited = \( \frac{4}{9} \times 360 = 160 \)
- Female employees recruited = \( \frac{5}{9} \times 360 = 200 \)

### Step 4: Calculate the total number of male and female employees after recruitment
After recruitment, the total number of male employees becomes:
\[ 9x + 160 \]
And the total number of female employees becomes:
\[ 7x + 200 \]

### Step 5: Set up the equation based on the new ratio
After recruitment, the new ratio of male to female employees is given as 61:55. Therefore, we can set up the equation:
\[ \frac{9x + 160}{7x + 200} = \frac{61}{55} \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 55(9x + 160) = 61(7x + 200) \]
Expanding both sides:
\[ 495x + 8800 = 427x + 12200 \]

### Step 7: Rearranging the equation
Rearranging the equation to isolate \( x \):
\[ 495x - 427x = 12200 - 8800 \]
\[ 68x = 3400 \]
\[ x = \frac{3400}{68} = 50 \]

### Step 8: Find the initial number of male and female employees
Now substituting \( x \) back into the expressions for male and female employees:
- Male employees = \( 9x = 9 \times 50 = 450 \)
- Female employees = \( 7x = 7 \times 50 = 350 \)

### Step 9: Calculate the difference between male and female employees
The difference between the number of male and female employees before recruitment is:
\[ 450 - 350 = 100 \]

### Final Answer
The difference between the male and female employees before recruitment is **100**.

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