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 \dfrac{d}{s} for this larger value of n?
Answer Choices
A. \dfrac{6}{25}
B. \dfrac{1}{4}
C. \dfrac{9}{25}
D. \dfrac{7}{16}
E. \dfrac{9}{16}