Explanation

(d) $t \propto \frac{f^{2}}{d^{2}}$
$\frac{f}{d}\ $means that the diameter of aperture is $\frac{f}{2}$
Now,$\ \frac{1}{100} \propto \frac{f^{2}}{\left( \frac{f}{2} \right)^{2}}$
Or $\frac{1}{100} \propto 4\ \ $…(i)
Again, $t \propto \frac{f^{2}}{\left( \frac{f}{8} \right)^{2}}$
Or $\ \ t \propto 64$ …(ii)
Dividing Eq.(ii) by Eq.(i)
$100t = \frac{64}{4} = 16\ or\ t = \frac{16}{100}s$