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 average number female in B & C?

Options

A. 480
B. 420
C. 520
D. 540

Answer

To solve the problem step by step, we will analyze the information provided and calculate the required values.

### Step 1: Calculate Total Female Employees in A and B
The average number of female employees who represent companies A and B is given as 420. Therefore, the total number of female employees in A and B can be calculated as:
\[ \text{Total female employees in A and B} = 420 \times 2 = 840 \]

**Hint:** To find the total from an average, multiply the average by the number of entities (in this case, companies).

### Step 2: Set Up Equations for Male and Female Employees
Let the number of male employees in company A be \(X\). Then, the number of male employees in company B will be \(1620 - X\) (since the total male employees in A and B is 1620).

According to the problem:
- The number of female employees in A is \(\frac{2}{3}X\).
- The number of female employees in B is \(\frac{2}{5}(1620 - X)\).

### Step 3: Create an Equation for Female Employees
The total number of female employees in A and B can be expressed as:
\[ \frac{2}{3}X + \frac{2}{5}(1620 - X) = 840 \]

**Hint:** Combine the expressions for female employees from both companies to form an equation.

### Step 4: Solve the Equation
To solve the equation, we first find a common denominator (which is 15):
\[ \frac{10X}{15} + \frac{2(1620 - X)}{15} = 840 \]
This simplifies to:
\[ 10X + 3240 - 2X = 12600 \quad (\text{Multiplying through by 15}) \]
Combining like terms gives:
\[ 8X + 3240 = 12600 \]
Subtracting 3240 from both sides:
\[ 8X = 9360 \]
Dividing by 8:
\[ X = 1170 \]

**Hint:** Isolate the variable by performing inverse operations.

### Step 5: Calculate Male and Female Employees in A and B
Now that we have \(X\):
- Male employees in A = \(1170\)
- Male employees in B = \(1620 - 1170 = 450\)

Now, calculate the female employees:
- Female employees in A = \(\frac{2}{3} \times 1170 = 780\)
- Female employees in B = \(\frac{2}{5} \times 450 = 180\)

### Step 6: Calculate Total Female Employees in C
The total female employees in C are 25% more than those in A:
\[ \text{Female employees in C} = 780 + 0.25 \times 780 = 780 \times 1.25 = 975 \]

**Hint:** To find a percentage increase, multiply the original number by (1 + percentage increase).

### Step 7: Calculate Total Male Employees in C
The total male employees in C are 33.33% more than those in B:
\[ \text{Male employees in C} = 450 + \frac{1}{3} \times 450 = 450 \times \frac{4}{3} = 600 \]

### Step 8: Calculate Average Number of Female Employees in B and C
Finally, we find the average number of female employees in B and C:
\[ \text{Average} = \frac{\text{Female in B} + \text{Female in C}}{2} = \frac{180 + 975}{2} = \frac{1155}{2} = 577.5 \]

**Hint:** To find the average, sum the values and divide by the number of values.

### Conclusion
The average number of female employees in B and C is **577.5**.