The mean age of employees in a company is 35 years. The mean ages of male and female workers are 38 and 33, respectively. If there are no transgender workers in the company, the percentage of male workers is

Given:

The mean age of all employees = 35 years.

The mean age of male workers = 38 years.

The mean age of female workers = 33 years.

Formula used:

Let the number of male workers be M, and the number of female workers be F.

Mean age of all employees = (Total age of males + Total age of females) / (M + F)

Calculations:

We know the total age of males = 38M and the total age of females = 33F.

The total age of all employees = 38M + 33F.

We also know the mean age of all employees is 35, so:

35 = (38M + 33F) / (M + F)

⇒ 35(M + F) = 38M + 33F

⇒ 35M + 35F = 38M + 33F

⇒ 35M - 38M = 33F - 35F

⇒ -3M = -2F

⇒ 3M = 2F

⇒ M/F = 2/3

This means the number of male workers is 2/3 of the number of female workers.

Now, let's find the percentage of male workers:

The total number of employees = M + F = (2/3)F + F = (5/3)F.

Percentage of male workers = (M / (M + F)) × 100

⇒ Percentage of male workers = ((2/3)F / (5/3)F) × 100

⇒ Percentage of male workers = (2 / 5) × 100

⇒ Percentage of male workers = 40%

∴ The percentage of male workers is 40%.