Ctibor marked a square plot on the map $\mathrm{s}$ with a scale of 1:50000 and calculated that its side in reality corresponds to $1 \mathrm{~km}$. He reduced the map on a photocopier so that the marked square had an area $1.44 \mathrm{~cm}^{2}$ smaller than originally.

What was the scale of the thus reduced map?

(M. Petrová)

Hint. What were the dimensions of the marked plot on the original map?
On the original map, the side of the plot had a length of $2 \mathrm{~cm}(2 \mathrm{~cm} \cdot 50000=$ $=100000 \mathrm{~cm}=1 \mathrm{~km})$. Thus, the area of the corresponding square was $4 \mathrm{~cm}^{2}$.

After reducing the map, the area of the new square was $2.56 \mathrm{~cm}^{2}(2.56+1.44=4)$. Therefore, the side of this square had a length of $1.6 \mathrm{~cm}\left(1.6^{2}=2.56\right)$.

These $1.6 \mathrm{~cm}$ on the map still correspond to the same $1 \mathrm{~km}$ in reality. The scale of the thus reduced map was therefore

$$
1.6: 100000=1: 62500 \text {. }
$$