4. One of the digits of a four-digit number is zero. When the zero is erased, the number is reduced by nine times. In which position is the zero? Find such numbers.
4. A four-digit number, one of the digits of which is zero, can have the form:

![](https://cdn.mathpix.com/cropped/2024_05_21_e53d4ff4f2278a1c0d12g-075.jpg?height=54&width=351&top_left_y=1889&top_left_x=855)

The last number can be immediately excluded, as in this case, the number $\boldsymbol{\text { a }}$ s will be 10 times smaller than the number $\boldsymbol{a} \boldsymbol{c} \boldsymbol{c} \mathbf{0}$, which contradicts the condition. We obtain that

$$
a 0 \kappa c=a \kappa c \times 9, a \kappa 0 c=a \kappa c \times 9 .
$$

Let's determine the last digit. Since $c x 9$ must result in a two-digit number with the units digit $\boldsymbol{c}$, then $\boldsymbol{c}=\mathbf{5}$, and we get:

$$
a 0 \kappa 5=a \kappa 5 \times 9, a \kappa 05=a \kappa 5 \times 9 .
$$

By conducting similar reasoning for the digits $\kappa$ and $\boldsymbol{a}$, we find the pair of numbers 2025 and 6075.

Answer: $2025,6075$.