13.005. The sum of the digits of a two-digit number is 12. If 36 is added to the desired number, the result is a number written with the same digits but in reverse order. Find the number.
## Solution.

Let the desired number be of the form $10x + y$. Then, according to the condition, $x + y = 12$ (1) and $10x + y + 36 = 10y + x$, i.e., $x - y + 4 = 0$ (2). Adding (1) and (2), we get $2x = 8$, from which $x = 4$, and $y = 8$.

Answer: 48.