1. Due to the price reduction of $20 \%$, with 2400 denars, one can buy one more book than with 2700 denars before the price reduction. What was the price of one book before the price reduction?
Solution: Let $x$ be the price before the reduction. Then for 2700 den., $\frac{2700}{x}$ books can be bought. After the $20 \%$ reduction, the price is $\frac{80}{100} x=\frac{4}{5} x$, so with 2400 den., $\frac{2400}{\frac{4}{5} x}$ books can be bought, i.e., $\frac{3000}{x}$ books. According to the condition of the problem, we get $\frac{3000}{x}-\frac{2700}{x}=1 ; \frac{300}{x}=1$, i.e., $x=300$. Therefore, the price of one book before the reduction is 300 denars.