Joint-stock company

In a joint-stock company workers were employed, divided into two categories according to the degree of automation of the production processes. In the workshop with a low degree of automation of production processes worked 25% of all workers, and in this department the average wage was 545 euros. The rest of the workers worked in the workshop with a high degree of automation. We further know that the average wage of all workers from both workshops was 835 euros. At the beginning of this year, an increase of the wages of the workers working in the workshop with a low degree of automation took place uniformly by 25€. By how many percent did the average wage in the entire joint-stock company grow as a result of the increase of the wages in this one group of workers?

Final Answer:

p =  0.7485 %

Step-by-step explanation:

$$\begin{gathered} X=545\text{eur} \\ Y=835\text{eur} \\ Y=0.25\cdot X+0.75\cdot a \\ b=0.25\cdot (X+25)+0.75\cdot a \\ 835=0.25\cdot 545+0.75\cdot a \\ b=0.25\cdot (545+25)+0.75\cdot a \\ 0.75a=698.75 \\ 0.75a-b=-142.5 \\ Row2-Row1\to Row2 \\ -b=-841.25 \\ b=\frac{-841.25}{-1}=841.25 \\ a=\frac{698.75}{0.75}=931.66666667 \\ a=\frac{2795}{3}\doteq 931.666667 \\ b=\frac{3365}{4}=841.25 \\ p=100\cdot \frac{b-Y}{Y}=100\cdot \frac{841.25-835}{835}=0.7485\% \end{gathered}$$

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