If the total number of workers remains the same in the year 2005 and the year 2006, then find the ratio between the total number of male managers in these two years.

Let the total number of employees in the the year 2005 be x

So, the total number of managers in 2005 = (80/100) × x = 0.8x

⇒ Total number of workers in 2005 = x – 0.8x = 0.2x

Hence, the number of male managers in 2005 = (5/8) × 0.8x = 0.5x

And the total number of employees in the the year 2006 be y

Also, So, the total number of managers in 2006 = (50/100) × y = 0.5y

⇒ Total number of workers in 2006 = y – 0.5y = 0.5y

Hence, the number of male managers in 2006 = (2/5) × 0.5y = 0.2y

As the number of workers is the same, we get:

0.2x = 0.5y

⇒ x = 2.5y      ----(i)

Using equation(i), the required ratio will become:

(0.5 × 2.5y)/0.2y = 25/4

∴ The reuqired ratio between the number of male managers in 2005 and 2006 is 25 ∶ 4