For a given angle of projection if the maximum height reached by a projectile is increased by 10% the horizontal range will

$h\propto u^2$ 

$\frac{dh}{h}=2\left(\frac{du}{u}\right)$

$10\%=2\frac{du}{u}$

$\frac{du}{u}=5\%$

Also $R\propto u^2$

$\frac{dR}{R}=2\left(\frac{du}{u}\right)=2\left(5\%\right)=10\%$

Also, we observe that R and H both are proportional to $u^2$, so R also gets an increment of 10%.