AMC 8 2020 Problem 24

A large square region is paved with $n^2$ gray square tiles, each measuring $s$ inches on a side. A border $d$ inches wide surrounds each tile. The figure below shows the case for $n=3$. When $n=24$, the $576$ gray tiles cover $64\%$ of the area of the large square region. What is the ratio $\frac{d}{s}$ for this larger value of $n?$

$\textbf{(A) }\frac{6}{25} \textbf{(B) }\frac{1}{4} \textbf{(C) }\frac{9}{25} \textbf{(D) }\frac{7}{16} \textbf{(E) }\frac{9}{16}$