How to determine (lost) surface (km²) of a country when both population and population density have changed? I am not sure if the question suits in this stack board, but I give it a try.

Let's assume there is a country with a population of 327 million people and a surface of 9.6 million km², resulting in 34 inhabitants per km². 

Now, let's say we have a fictive war scenario, in which the country loses and has to give up land to the victors. The population sunk to 100 million people and 10 inhabitants per km² (still assuming that surface was given to victors, thus the country now has a smaller surface!!). How would I calculate the new surface with these two (now changed) variables or would I need more data?

My question now is: 

Is it still possible to determine the new surface of the country when both population and population density changed? 

I tried many ways to accomplish that, but I really have no idea how to approach it. Maybe it's possible with a system of linear equations? I have no idea.
$\text{Poulation density} = \frac{\text{Population}}{\text{Surface}}$

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.