In a factory, $a$ workers were employed. One day, $b$ workers left the factory for agricultural work. By what percentage do the remaining workers need to increase their average daily productivity if they want to meet their original production targets?
1. Task. In a plant, "a" workers were working. One day, b workers left the plant for fieldwork. By what percentage must the remaining workers increase their average daily productivity if they want to meet the original production plan?

I. Solution. If the entire work is done by the original $a$ workers, each of them gets $1 / a$ of the work. Since only $a-b$ workers are working on the day in question, each of them gets $1 /(a-b)$ of the work for that day. Thus, each worker must produce an additional part of the work:

$$
\frac{1}{a-b}-\frac{1}{a}=\frac{b}{a(a-b)}
$$

This part is a fraction of the planned $1 / a$:

$$
100 \frac{b}{a(a-b)}: \frac{1}{a}=\frac{100 b}{a-b}
$$

percentage. Since $a>b>0$, the result obtained is positive.

II. Solution. Let's take the unit of work to be the daily productivity of 1 worker according to the original plan. Thus, the missing work from the absentees is $b$ units per day, and each of the remaining $a-b$ workers gets an additional $b /(a-b)$ units of work per day, which is the amount by which they must increase their daily productivity. This is $\frac{100 b}{a-b}$ percent of the planned daily productivity of 1 unit.