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.

Calculate the difference between the total number of male employees and the total number of female employees across enterprise K.

The correct answer is 31.

Let us break down the given information step-by-step to find the total number of male and female employees in each branch of Enterprise K.

Step 1: Formulate expressions for Branch A and Branch C employees
The ratio of male to female employees in Branch A is 7:10.
Let the number of male employees in Branch A be $7x$ and the number of female employees in Branch A be $10x$.

The number of female employees in Branch C is 20% more than that in Branch A:
Female employees in Branch C = $10x\times 1.20=12x$

The number of male employees in Branch C is 6 more than the number of female employees in Branch C:
Male employees in Branch C = $12x+6$

Step 2: Determine the value of x
We are given that the average number of male employees across all three branches is 39.
Total male employees across all 3 branches = $39\times 3=117$
The number of male employees in Branch B is given as 35.
Summing the male employees from all three branches:
$\left(\text{Male in A}\right)+\left(\text{Male in B}\right)+\left(\text{Male in C}\right)=117$
$7x+35+(12x+6)=117$
$19x+41=117$
$19x=117-41$
$19x=76$
$x=4$

Step 3: Calculate male and female employees in each branch
Substituting $x=4$ into our expressions:
• Branch A:
Male employees = $7\times 4=28$
Female employees = $10\times 4=40$

• Branch B:
Male employees = 35
Female employees are 25% more than female employees in Branch C.
Female employees in Branch C = $12\times 4=48$
Female employees in Branch B = $48\times 1.25=60$

• Branch C:
Male employees = $48+6=54$
Female employees = 48

Step 4: Find the total number of male and female employees and their difference
Total male employees = $28+35+54=117$
Total female employees = $40+60+48=148$
Difference between total female and total male employees = $148-117=31$

Therefore, the difference between the total number of male employees and the total number of female employees across enterprise K is 31.