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.

The number of female employees in Branch B is what percent more or less than the number of female employees in Branch A?

Correct Answer: The correct answer is 50%.

Step-by-Step Explanation:

Step 1: Define variables for Branch A
The ratio of male to female employees in Branch A is given as 7:10.
Let the number of male employees in Branch A be M_A and the number of female employees in Branch A be F_A.
We can express these using a common multiplier x:
$M_A=7x$

$F_A=10x$

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:
$F_C=10x\times (1+0.20)=12x$
The number of male employees in Branch C (M_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
We are given that:
• Male employees in Branch B (M_B) = 35
• Average number of male employees across all three branches = 39
Therefore, total male employees across all three branches:
$\text{Total male employees}=39\times 3=117$
Now, form an equation combining male employees from all three branches:
$M_A+M_B+M_C=117$
Substitute the expressions for M_A, M_B, and M_C:
$7x+35+(12x+6)=117$
Simplify and solve for x:
$19x+41=117$

$19x=117-41$

$19x=76$

$x=\frac{76}{19}=4$

Step 4: Find female employee counts for Branch A, C, and B
Female employees in Branch A:
$F_A=10x=10\times 4=40$
Female employees in Branch C:
$F_C=12x=12\times 4=48$
Female employees in Branch B (F_B) is 25% more than female employees in Branch C:
$F_B=48\times (1+0.25)=48\times 1.25=60$

Step 5: Calculate the required percentage difference
We need to find by what percent the female employees in Branch B (60) are more than the female employees in Branch A (40):
$\text{Percentage More}=\frac{F_B-F_A}{F_A}\times 100\%$
Substitute the values into the formula:
$\text{Percentage More}=\frac{60-40}{40}\times 100\%=\frac{20}{40}\times 100\%=50\%$
Thus, the number of female employees in Branch B is 50% more than the number of female employees in Branch A.