#### Answer

No, the car does not exceed the speed limit in this case.

#### Work Step by Step

Conversion factor: 1 mile = 1.609 km.
The car traveling at $30\,\mathrm{km/h}$ has a speed of $18.64\,\mathrm{mi/h}$, which is less than the speed limit of $25\,\mathrm{mi/h}$.
Therefore, the statement that the car exceeds the speed limit is wrong.