## Task 1 - 040831

If the digits of a two-digit number $n$ are reversed, the resulting number is $\frac{8}{3}$ times as large as $n$. The number $n$ is to be determined.
It is given that

$$
\frac{8}{3}(10 x+y)=10 y+x \quad ; \quad 7 x=2 y
$$

Since $x$ and $y$ are natural numbers less than 10, it follows that $x=2$ and $y=7$. Therefore, the desired number is 27.