How to determine (lost) surface (km²) of a country when both population and population density have changed?
$\text{Poulation density} = \frac{\text{Population}}{\text{Surface}}$

Re-arranging 

$\text{Surface} = \frac{\text{Population}}{\text{Poulation density}}$

In your case

$\text{Surface} = \frac{100,000,000\, \text{inhabitants}}{10\, \text{inhabitants}\, \text{km}^{-2}}=10,000,000\, \text{km}^2$

So something doesn't make sense, because those numbers suggests that the surface of the country is now larger than before.