Let the aircrafts fuel weight be ‘f’ and aircraft structural weight be ‘s’.The jet aircraft’s range is proportional to

\(\sqrt{s+f}-\sqrt{s}\)

Therefore fractional reduction in range is

\(\frac{\sqrt{s+f}-\sqrt{s+0.9f}}{\sqrt{s+f}-\sqrt{s}}\)

If  \(f/s\sim 1 \)

\(\frac{\Delta R}{R}=\frac{\sqrt{2}-\sqrt{1.9f}}{\sqrt{2}-\sqrt{1}}
\\=8.6 \%\)

If \(f/s<<1\) using binomial expansion  we find that  \(\frac{\Delta R}{R}\) converges to 10 %.

For propeller aircraft the range is proportional to \(ln\left ( 1+\frac{f}{w} \right )\)

\(\frac{\Delta R}{R}=\frac{ln\left ( \frac{s+f}{s+0.9f} \right )}{ln\left ( \frac{s+f}{s} \right )}\)

If \(f/s\sim 1\) then reduction in range will be 7.4 %

If \(f/s\sim 0\) using series expansion for logarithm this converges to 10 %.

Therefore we see that in all these cases reduction in range is less than 10 %.