3.23 A team of workers completed a certain task. If the team is reduced by 20 people, then the same task will be completed 5 days later than with the original composition, and if the team is increased by 15 people, then the task will be completed 2 days earlier. How many workers were originally in the team and how many days did they take to complete the task?
3.23 Let $x$ workers completed the task in $y$ days; then according to the condition $x y=(x-20)(y+5)$ and $x y=(x+15)(y-2)$. We can write both equations as proportions:

$\frac{x-20}{x}=\frac{y}{y+5}$ and $\quad \frac{x+15}{x}=\frac{y}{y-2}$.

Each proportion of the form $\frac{a}{b}=\frac{c}{d}$ can be replaced by an equivalent proportion of the form $\frac{a-b}{b}=\frac{c-d}{d}$. Then we get

$\frac{-20}{x}=\frac{-5}{y+5}$ and $\frac{15}{x}=\frac{2}{y-2}$.

Now it is easy to find that $x=60$ and $y=10$. Thus, there were 60 people in the team, who completed the task in 10 days.

Answer: 60 workers; 10 days.