## Task 4 - 140734

In a VEB, a certain type of workpiece was first processed in department A1 and then in department A2. Initially, the same number of workpieces could be processed daily in one department as in the other.

With the help of rationalization measures in both departments, the 53 workers in department A1 increased their production to 159%, and the 62 workers in department A2 increased their production to 124%. However, because the production output in both departments had to be the same, a sufficient number of workers from one department decided to work in the other department.

How many workers from which of the two departments took up work in the other department, so that the production output in both departments was again the same?

By what percentage of the production volume before the rationalization measures did the total production output increase?

Notes: It is assumed that the production output of both departments is proportional to the number of workers.
In A1, after the rationalization, each of the 53 workers produced $\frac{1.59}{53}$ and in A2 each of the 62 workers produced $\frac{1.64}{62}$ of their department's production output before the rationalization measures. Since the production in A1 had grown to a larger amount than in A2, workers had to move from A1 to A2. Let the number of these workers be $x$. Afterwards, the production in A1 was $\frac{1.59}{53}(53-x)$ of the previous production, and in A2 it was $\frac{1.24}{62}(62+x)$. Since these two production outputs were equal, we have

$$
\frac{159}{53}(53-x)=\frac{124}{62}(62+x) \Rightarrow x=7
$$

Thus, 7 workers moved from A1 to A2. The new production output in each department then amounted to $\frac{1.59}{53} \cdot 46=1.38$, i.e., it increased to $138\%$ of the previous production output.