A block takes twice as much time to slide down a 45° rough inclined plane as it takes to slide down a similar smooth plane. The coefficient of friction is:

By using 2^nd equation of motion s = ut + (½) at²
For smooth inclined plane :$\mathrm{s}=0+\frac{1}{2}(\mathrm{gsin}\mathrm{\theta }){\mathrm{t}}_1^2$
For sough inclined plane :$\mathrm{s}=0+\frac{1}{2}(\mathrm{gsin}\mathrm{\theta }-\mathrm{\mu gcos}\mathrm{\theta }){\mathrm{t}}_2^2$
$\mathrm{But} {\mathrm{t}}_2=2{\mathrm{t}}_1 \mathrm{so} \mathrm{\mu }=\frac{3}{4}$