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 option is 31.

Step-by-step Explanation:

1. Analyze 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:

$F_A=10x$

2. Analyze Branch C:

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

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

The number of male employees in Branch C ($M_C$) is 6 more than the number of female employees in Branch C:

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

3. Calculate the value of $x$:

The average number of male employees across all three branches (A, B, and C) is 39.

Total number of male employees across enterprise K:

$39\times 3=117$

We are given that the number of male employees in Branch B ($M_B$) is 35. Therefore, the sum of male employees in Branch A and Branch C is:

$M_A+M_C=117-35=82$

Substitute $M_A=7x$ and $M_C=12x+6$ into the equation:

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

$19x+6=82$

$19x=82-6$

$19x=76$

$x=4$

4. Calculate the number of employees in each branch:

Branch A:
Male employees: $M_A=7\times 4=28$
Female employees: $F_A=10\times 4=40$

Branch C:
Female employees: $F_C=12\times 4=48$
Male employees: $M_C=48+6=54$

Branch B:
Male employees: $M_B=35$
Female employees ($F_B$) are 25% more than female employees in Branch C:
$F_B$=48+(0.25×48)=48+12=60

5. Find total male and female employees and their difference:

Total male employees across enterprise K:

$\text{Total Males}=28+35+54=117$

Total female employees across enterprise K:

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

Difference between total female and male employees:

$\text{Difference}=148-117=31$

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