With all due respect, I think the calculation does work. You are making the fundamental mistake of confusing volume (Liters) with Weight (Kg). If you mix 1 Kg of a substance into 9 L of water, the only circumstance in which you would get 10 L of solution would be if the density (weight /volume) of that substance was equal to the density of water. In the case of sugar, it is considerably denser than water, so mixing 1 Kg sugar with 9 L water will give the solution a weight of 10 Kg, but a volume less than 10 L.

It is relatively simple to calculate the theoretical volume of the solution.

First, mix 1 Kg sugar in 9 L water. This gives 10 Kg of solution at 10 degrees Plato.

Then use http://www.brewersfriend.com/plato-t...version-chart/ to look up the specific gravity of the solution. (You could also use other calculators, but the linked chart provides the formula used to apply the conversion.)

You will find that the S.G. of the solution is 1.040

Using the definition of specific gravity (http://en.wikipedia.org/wiki/Specific_gravity), you can calculate the volume of the solution Volume = Weight / specific gravity * density of water i.e 10 Kg / 1.040 * 1.000 = 9.615 Liters

Note, I have not applied temperature compensation to these figures as you did not specify temperatures.

-a.