32. Two identical two-digit numbers were written on the board. To one of them, 100 was added to the left, and to the other, 1 was added to the right, as a result of which the first number became 37 times larger than the second. What numbers were written on the board?
32. When multiplying the second number, ending with the digit 1, by 37, we get a number ending with the digit 7. This means the original numbers ended with the digit 7, i.e., $\overline{a 7}$. According to the condition, $\overline{100 a 7}=\overline{a 71} \cdot 37$, $\overline{a 71} \cdot 37=(100 a+71) \cdot 37=3700 a+2627$. It is easy to notice that $a=2$. Indeed, $3700 \cdot 2=7400,7400+2627=10027$. Therefore, the number written on the board was $27,27$.