jmc

The ratio of the radius of the smaller circle to that of the larger circle is $\frac{1}{2}$, since the diameter is half as long. Thus, the ratio of the area of the smaller circle to that of the larger circle is ${\left(\frac{1}{2}\right)}^2=\frac{1}{4}$. Thus, the gray area is $\boxed{25\%}$ of the area of the larger circle.

To be more rigorous: if the radius of the larger circle is $r$, the radius of the smaller circle is $\frac{1}{2}r$. Thus, the ratio of the area of the smaller to the larger is: $\frac{\pi (\frac{1}{2}r{)}^2}{\pi r^2}=\frac{1}{4}$.