Two polaroids are crossed to each other.  Now, one of them is rotated through 60°. The percentage of incident unpolarised light that passes through the system will be

Initially they are at 90⁰.  If one of them is rotated through 60⁰. Then the angle between them becomes 30⁰.

Plane of polarisation of first emergent ray and the axis of transmission of second polaroid becomes 30⁰.$\Rightarrow \mathrm{I}=\frac{{\mathrm{I}}_0}{2}{\cos }^2\mathrm{\theta }=\frac{{\mathrm{I}}_0}{2}{\cos }^2{30}^0$

$\Rightarrow \frac{\mathrm{I}}{{\mathrm{I}}_0}=\frac{3}{8}=0.375\Rightarrow \frac{\mathrm{I}}{{\mathrm{I}}_0}\mathrm{\%}=37.5\mathrm{\%}$