The bookstore receives a discount from the publisher, which, expressed as a percentage, is 1.5 times smaller than the profit percentage. What is the discount as a percentage of the purchase price?
Let the selling price of the book be $a$ and the discount be $x \%$. The bookseller pays $a-\frac{a x}{100}=a\left(1-\frac{x}{100}\right)$ pengő for the book. They sell it with a profit of $1.5 x \%$, that is,

$$
a\left(1-\frac{x}{100}\right)\left(1+\frac{1.5 x}{100}\right) \text{ pengő, }
$$

and thus the selling price of the book is: $a\left(1-\frac{x}{100}\right)\left(1+\frac{1.5 x}{100}\right)=a$.

$$
(100-x)(100+1.5 x)=10000 \text{ or } 50 x-1.5 x^{2}=0 .
$$

From this,

$$
x_{1}=0, \quad x_{2}=\frac{100}{3}=33 \frac{1}{3}
$$

The discount is $33 \frac{1}{3} \%$ of the selling price, the purchase price is $66 \frac{2}{3} \%$ of the selling price, and the profit is $50 \%$ of the purchase price, that is, $1.5 \cdot 33 \frac{1}{3} \%$.