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.
Let the number of male and female employees in Branch A be based on the given ratio 7:10.
Male employees in Branch A ($M_A$) = $7x$
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 ($F_C$) 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 ($M_C$) is six more than the female employees in Branch C:
$M_C=12x+6$

Step 3: Calculate $x$ using male employee data.
The average number of male employees across all three branches is 39.
Total male employees across three branches = $39\times 3=117$
Given male employees in Branch B ($M_B$) = 35.
Now, set up the total male employees equation:
$M_A+M_B+M_C=117$
$7x+35+12x+6=117$
$19x+41=117$
$19x=117-41$
$19x=76$
$x=4$

Step 4: Find female employees in each branch.
Female employees in Branch A ($F_A$) = $10\times 4=40$
Female employees in Branch C ($F_C$) = $12\times 4=48$
Female employees in Branch B ($F_B$) are 25% more than in Branch C:
$F_B=48+0.25\times 48=48+12=60$

Step 5: Determine the average number of female employees across all three branches.
Total female employees across three branches = $F_A+F_B+F_C=40+60+48=148$
Average female employees = $\frac{148}{3}=49\frac{1}{3}$