Given data shows total male and female employee in three companies in a seminar. Read data carefully and answer the questions:
In annual seminar of three companies, A, B and C some male and female employees represent their companies. Average number of female employees who represent A and B is 420. Total male employee in A and B is 1620. Number of female employees is `(2)/(3)` rd and `(2)/(5)` th of male employee in A and B respectively. Total female employee who represent C are 25% more than total female employee who represent A and total male employee who represent C are 33 `(1)/(3)%` more than total female employee who represent B.
Find difference between Total male employees who represent C and total female employee who represent B?

Options

A. 120
B. 140
C. 100
D. 160

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Define Variables
Let:
- \( M_A \) = Number of male employees in Company A
- \( M_B \) = Number of male employees in Company B
- \( F_A \) = Number of female employees in Company A
- \( F_B \) = Number of female employees in Company B
- \( M_C \) = Number of male employees in Company C
- \( F_C \) = Number of female employees in Company C

### Step 2: Set Up Equations
From the problem statement, we have the following equations based on the information given:

1. **Total Male Employees in A and B**:
\[ M_A + M_B = 1620 \]

2. **Average Female Employees in A and B**:
\[ \frac{F_A + F_B}{2} = 420 \implies F_A + F_B = 840 \]

3. **Female Employees in A**:
\[ F_A = \frac{2}{3} M_A \]

4. **Female Employees in B**:
\[ F_B = \frac{2}{5} M_B \]

### Step 3: Substitute and Solve for \( M_A \) and \( M_B \)
Substituting \( F_A \) and \( F_B \) into the equation \( F_A + F_B = 840 \):

\[ \frac{2}{3} M_A + \frac{2}{5} M_B = 840 \]

To eliminate the fractions, find a common denominator (15):

\[ 10 M_A + 6 M_B = 12600 \quad \text{(Multiplying the entire equation by 15)} \]

Now we have two equations:
1. \( M_A + M_B = 1620 \)
2. \( 10 M_A + 6 M_B = 12600 \)

### Step 4: Solve the System of Equations
From the first equation, express \( M_B \):
\[ M_B = 1620 - M_A \]

Substituting \( M_B \) into the second equation:

\[ 10 M_A + 6(1620 - M_A) = 12600 \]
\[ 10 M_A + 9720 - 6 M_A = 12600 \]
\[ 4 M_A + 9720 = 12600 \]
\[ 4 M_A = 12600 - 9720 \]
\[ 4 M_A = 2880 \implies M_A = 720 \]

Now substituting \( M_A \) back to find \( M_B \):
\[ M_B = 1620 - 720 = 900 \]

### Step 5: Calculate Female Employees
Now, using \( M_A \) and \( M_B \) to find \( F_A \) and \( F_B \):
\[ F_A = \frac{2}{3} \times 720 = 480 \]
\[ F_B = \frac{2}{5} \times 900 = 360 \]

### Step 6: Calculate Female Employees in Company C
Total female employees in Company C are 25% more than those in A:
\[ F_C = F_A + 0.25 F_A = 480 + 120 = 600 \]

### Step 7: Calculate Male Employees in Company C
Total male employees in Company C are 33⅓% more than total female employees in Company B:
\[ M_C = F_B + \frac{1}{3} F_B = 360 + 120 = 480 \]

### Step 8: Find the Difference
Finally, we need to find the difference between total male employees in Company C and total female employees in Company B:
\[ \text{Difference} = M_C - F_B = 480 - 360 = 120 \]

### Final Answer
The difference between total male employees who represent C and total female employees who represent B is **120**.

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