The ratio of male to female employees in a company is 8:6. If 15 more female employees join the company, the new ratio of male to female employees becomes 8:7. What is the total number of employees in the company initially?

The correct answer is 210.

Step 1: Understand the initial ratio and define variables

The initial ratio of male to female employees is given as 8:6.

Let the common ratio multiplier be $x$.

Therefore:

Initial number of male employees = $8x$

Initial number of female employees = $6x$

Step 2: Calculate the total initial number of employees

The total initial number of employees is the sum of male and female employees:

$\text{Total initial employees}=8x+6x=14x$

Step 3: Set up an equation using the new ratio

When 15 more female employees join the company, the number of female employees becomes $6x+15$.

The number of male employees remains unchanged at $8x$.

The new ratio of male to female employees becomes 8:7. We can set up the proportion:

$\frac{8x}{6x+15}=\frac{8}{7}$

Step 4: Solve for $x$

Dividing both sides of the numerator by 8:

$\frac{x}{6x+15}=\frac{1}{7}$

Cross-multiplying gives:

$7x=6x+15$

Subtracting $6x$ from both sides:

$x=15$

Step 5: Find the initial total number of employees

Substitute $x=15$ back into the total initial employees expression $14x$:

$\text{Total initial employees}=14\times 15=210$

Thus, the initial total number of employees in the company was 210.