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.

Carefully study the details provided below and answer the following question.

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 ratio of the number of male employees in Branch A to the number of female employees in Branch C.

Correct Answer: 7:12

Let us solve the problem step-by-step by defining variables for the number of male and female employees in each branch.

Step 1: Express the employees in Branch A in terms of a variable.

Given that the ratio of male to female employees in Branch A is 7:10, we can define:

The number of male employees in Branch A = $7x$

The number of female employees in Branch A = $10x$

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

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

Female employees in Branch C = $10x+(0.20\times 10x)=12x$

Step 3: Determine the required ratio.

We need to find the ratio of the number of male employees in Branch A to the number of female employees in Branch C:

$\text{Ratio}=\frac{\text{Male employees in Branch A}}{\text{Female employees in Branch C}}$

Substituting the values in terms of $x$:

$\text{Ratio}=\frac{7x}{12x}$

Canceling out the common variable $x$ from the numerator and denominator gives:

$\text{Ratio}=\frac{7}{12}$

Thus, the ratio of male employees in Branch A to female employees in Branch C is 7:12.

Verification:

We can also verify this by calculating the exact value of $x$:

Male employees in Branch C = $12x+6$

Male employees in Branch B = 35

Average number of male employees across all three branches = 39

Total male employees = $39\times 3=117$

Summing the males from all three branches:

$7x+35+12x+6=117$

$19x+41=117$

$19x=76$

$x=4$

Now calculating actual numbers:

Male employees in Branch A = $7\times 4=28$

Female employees in Branch C = $12\times 4=48$

Required Ratio = $28:48=7:12$