"The ratio of the number of male staff to the number of female staff is 2:3."
This means if
is the number of male staff, and
is the number of female staff, then these numbers occur in a fixed ratio such that
![\frac xy = \frac23](https://img.qammunity.org/2023/formulas/mathematics/high-school/5rysdzxiuzgmkycwjk3feccvfwzx45kes6.png)
The sentence does not say anything about the actual number of staff members. There's no reason to believe that there are 50 people working.
What it does say is that 2/5 = 40% of the team is made of males and 3/5 = 60% is made of females.
(a) Of the males, 20% = 1/5 of them are under the age of 20. This means that 20% of 40% of the entire staff is made up of males under 20, or
2/5 × 1/5 = 2/25 = 8%
Of the females, 40% = 2/5 are under the age of 20. So 40% of 60% are females under 20, which comes out to
3/5 × 2/5 = 6/25 = 24%
Adding these up, we get a total of 8% + 24% = 32%.
(b) Yes, any change to the team would adjust this percentage.
Consider a smaller example of a team of 4, 1 each of male/female and under/over 20. 1/4 = 25% of this team is female and under 20. If we add one more under-20 female, the new ratio is 2/5 = 40%. If we add one more member to any other group, the new ratio is 1/5 = 20%.