Carefully analyze the given details and answer the question that follows.

There are three branches (Branch A, Branch B, and Branch C) in enterprise K. The ratio of male to female employees in Branch A is 7:10. The number of female employees in Branch C is 20% more than the number of female employees in Branch A. The number of male employees in Branch C is six more than that of female employees in Branch C. The average number of male employees across all three branches is 39 and the number of male employees in Branch B is 35. The number of female employees in Branch B is 25% more than the number of female employees in Branch C.

Determine the average number of female employees across all three branches.

The correct answer is:

$49\frac{1}{3}$

Step 1: Define variables for Branch A.

The ratio of male to female employees in Branch A is given as 7 : 10.

Let the common ratio multiplier be $x$.

Number of male employees in Branch A:

$M_A=7x$

Number of female employees in Branch A:

$F_A=10x$

Step 2: Express employees in Branch C in terms of $x$.

The number of female employees in Branch C is 20% more than the female employees in Branch A:

$F_C=10x+(0.20\times 10x)=12x$

The number of male employees in Branch C is 6 more than the female employees in Branch C:

$M_C=F_C+6=12x+6$

Step 3: Solve for $x$ using male employee data.

The average number of male employees across all three branches is 39.

Therefore, total male employees across branches A, B, and C:

$\text{Total Male Employees}=39\times 3=117$

We are given that male employees in Branch B:

$M_B=35$

Thus, the sum of male employees in Branch A and Branch C is:

$M_A+M_C=117-35=82$

Substituting the expressions for $M_A$ and $M_C$:

$7x+(12x+6)=82$

$19x+6=82$

$19x=76$

$x=4$

Step 4: Find the exact number of female employees in each branch.

1. Female employees in Branch A:

$F_A=10\times 4=40$

2. Female employees in Branch C:

$F_C=12\times 4=48$

3. Female employees in Branch B (25% more than Branch C):

$F_B=48+(0.25\times 48)=48+12=60$

Step 5: Calculate the average number of female employees across all three branches.

Total female employees across all 3 branches:

$\text{Total Females}=F_A+F_B+F_C=40+60+48=148$

Average number of female employees:

$\text{Average Females}=\frac{148}{3}=49\frac{1}{3}$