$\Rightarrow i=i_0\sin \omega t$

When $i=i_0$

$i_0=i_0\sin \omega t_1\Rightarrow \omega t_1=\frac{\pi }{2} \dots \left(1\right)$

When $i=\frac{i_0}{\sqrt{2}}$

$\frac{i_0}{\sqrt{2}}=i_0\sin \omega t_2\Rightarrow \omega t_2=\frac{\pi }{4} \dots \left(2\right)$

Time taken by current from maximum value to rms value, $\Rightarrow \left(t_1-t_2\right)=\frac{\pi }{2\omega }-\frac{\pi }{4\omega }=\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}$

$=\frac{1}{8\times 50}$

$=\frac{1}{400}\sec$

$=2.5 \mathrm{ms}$