An arithmetic sequence is a sequence of numbers in which the difference between each number and the one preceding it is always the same; this difference is called the common difference. (For example, 2, 8, 14, 20, 26, 32 is an arithmetic sequence with a common difference of 6.)

Bolek and Lolek each had their own arithmetic sequence. Both Bolk's and Lolek's sequences started with the number 2023 and ended with the number 3023. These two sequences had 26 common numbers. The ratio of Bolk's to Lolek's common difference was $5:2$.

Determine the difference between Bolk's and Lolek's common difference.

(E. Novotná)

Hint. Bolk's and Lolek's common differences can be expressed using one variable.
The ratio of Bolko's and Lolko's difference was $5: 2$. Thus, Bolko's difference was $5k$ and Lolko's $2k$, where $k$ is an unknown number that we will soon determine from other information. The difference between Bolko's and Lolko's difference can then be expressed as $5k - 2k = 3k$.

Bolko's, respectively, Lolko's sequence was

$$
\begin{aligned}
& \text { 2023, } \quad 2023+5k, \quad 2023+10k, \ldots \text {, } \\
& 2023, \quad 2023+2k, \quad 2023+4k, \quad 2023+6k, \quad 2023+8k, \quad 2023+10k, \quad \ldots,
\end{aligned}
$$

the common numbers of both sequences were

$$
2023, \quad 2023+10k, \quad 2023+20k, \quad 2023+30k, \quad \ldots
$$

There were 26 common numbers, and the last one was 3023. The 26th number in the sequence (*) is of the form $2023 + 250k$, so it must have been $k=4 (2023 + 250 \cdot 4 = 3023)$.

The difference between Bolko's and Lolko's difference was 12.