A Stakhanovist work method, with an innovation, reduces the time required to produce a certain workpiece by 1 minute, thereby increasing its performance expressed as a percentage of the norm by $20 \%$. How many minutes did it take to produce a workpiece before the innovation, and what was the performance in percentage at that time, if it already took 14 minutes and 24 seconds less to produce the workpiece; compared to what the norm requires?

Let the standard time for completing a workpiece be $x$ minutes. Before the improvement, it takes $x-14.4$ minutes, and after the improvement, it takes $x-15.4$ minutes to complete a workpiece.

Let the performance of the Stakhanovite before the improvement be $y \%$, then

$$
y: 100=\frac{1}{x-14.4}: \frac{1}{x}
$$

from which

$$
y=\frac{100 x}{x-14.4} \%
$$

The performance after the improvement is $\frac{100 x}{x-15.4} \%$ and according to the problem,

$$
\frac{100 x}{x-14.4}+20=\frac{100 x}{x-15.4}
$$

thus

$$
\begin{aligned}
& 5 x^{2}-174 x+1108.8=0 \\
& x_{1}=26.4 \quad \text { and } \quad\left[x_{2}=8.4\right]
\end{aligned}
$$

The second root is not valid as it leads to a negative working time. Therefore, the Stakhanovite completed a workpiece in $26.4-14.4=$ 12 minutes before the improvement, and the performance was $\frac{100 x}{x-14.4}=\frac{2640}{12}=220 \%$.

Ottó Árkossy (Csongrád, Batsányi g. II. o. t.)