I don't get it.
If you do it by weight:
90% of 20lb is 18lb.
10% of 20lb is 2lb.
For water to be 50% of mixture, water must = other = 2lb.
The total mixture would be 4lb.
If we do it by volume, well, we don't know what the volume is, but let us assume 20l.
Again we get 4l, 2l of each. The problem is, what is their relative densities? We don't know.
Thing is, 50% water is not a loss of 40% of the original volume. The 50% is measured to the new volume, not the old. I would think it would be closer to 10% water and 10% other stuff compared to the original volume.
Maybe it is something I am not seeing?