13.187. A team of workers was supposed to manufacture 8000 identical parts within a certain period. In fact, the work was completed 8 days ahead of schedule because the team produced 50 more parts daily than planned. What was the original deadline for completing the work, and what was the daily percentage of overachievement?
Solution.

Let the work was supposed to be completed in $x$ days. The team was supposed to produce $\frac{8000}{x}$ pieces daily, but they produced $\left(\frac{8000}{x}+50\right)$ pieces and worked for a total of $(x-8)$ days. Therefore, $\left(\frac{8000}{x}+50\right)(x-8)=8000$, from which $x=40$ days. The team was supposed to produce $\frac{8000}{40}=200$ pieces per day, but they produced $200+50=250, y=\frac{250 \cdot 100}{200}=125 \%$. Thus, the daily percentage of overachievement is $125-100=25 \%$.

Answer: 40 days; $25 \%$.