In a plant, 40 workers switch to the Stakhanovite method of work. As a result, the plant's production increases by $20 \%$. If, together with the first Stakhanovites, $60 \%$ of the workers switch to the new method, then this results in the plant's production increasing to two and a half times the original production. The question is, how many workers are there in the plant and by how many times does the plant's production increase if all workers learn the new method?
I. solution: Let the overproduction of a Stakhanovite be $x$ times the production of a worker using the old method, and the number of workers be $y$. Then, according to the problem,

$$
y+40 x=1.2 y
$$

and

$$
\begin{gathered}
y+0.6 y x=2.5 y . \\
\text{From (2)} \quad x=\frac{2.5-1}{0.6}=\frac{1.5}{0.6}=2.5
\end{gathered}
$$

Substituting this value of $x$ into (1)

$$
y+100=1.2 y
$$

from which

$$
y=500 \text{ workers}
$$

and the plant's production, if all workers switch to the new method, increases to $1+x=3.5$ times (350%) of the original.

II. solution: The overproduction of one Stakhanovite is $\frac{20}{40}=\frac{1}{2} \%$ of the plant's total production. The overproduction of 60% of the workers, according to the problem, is 150% of the total production, which implies that 60% of the workers (150 : $\left.{ }^{1} / 2=\right)$ represent 300 workers, so the total number of workers is 500, and thus the overproduction, if all 500 workers become Stakhanovites, is $500 \cdot 1 / 2=250 \%$, meaning the plant's production increases to 3.5 times its original value.