2.1. The master's day shift lasts $10 \%$ longer than the apprentice's shift. If the apprentice worked as long as the master, and the master worked as long as the apprentice, they would produce the same number of parts. By what percentage does the master produce more parts per day than the apprentice?
Solution. Let $p=10 \%$. Suppose the productivity of the apprentice is $a$ parts per hour, the master's productivity is $b$ parts per hour, the apprentice's workday is $n$ hours, and the master's workday is $m$ hours. Then from the condition it follows:

$$
m=n\left(1+\frac{p}{100}\right), \quad \text { and } \quad m a=n b \Rightarrow n\left(1+\frac{p}{100}\right) a=n b \Rightarrow b=\left(1+\frac{p}{100}\right) a .
$$

In a day, the master makes $b m-a n=\frac{p}{100}\left(2+\frac{p}{100}\right)$ an more parts than the apprentice, which as a percentage of the apprentice's daily output is

$$
\frac{p}{100}\left(2+\frac{p}{100}\right) a n \cdot \frac{100}{a n}=p\left(2+\frac{p}{100}\right)
$$

If $p=10 \%$, then $p\left(2+\frac{p}{100}\right)=21$.

Answer: 21. (C)

![](https://cdn.mathpix.com/cropped/2024_05_06_a8c31eb257d724803ce6g-02.jpg?height=67&width=727&top_left_y=1331&top_left_x=716)