Question 18

Explanation

We will determine the ratio of the number of male to female employees using the concept of combined average (weighted average).

Let:

• $n_L$ = number of male employees
• $n_P$ = number of female employees
• $\bar{x}_L = 320.000$ (average income of males)
• $\bar{x}_P = 285.000$ (average income of females)
• $\bar{x}_{comb} = 300.000$ (combined average income)

The formula for the combined average is:

Substitute the known values into the formula:

To simplify the calculation, divide all numbers by $1.000$:

Cross-multiply the denominator to the left side:

Group like terms:

Find the ratio $n_L : n_P$:

Thus, the ratio of the number of male to female employees is $3:4$.