A compass needle oscillates 20 times per minute at a place where the dip is 30^° and 30 times per minute where the dip is 60^°. The ratio of total…

A compass needle oscillates $\displaystyle 20$ times per minute at a place where the dip is $\displaystyle 30^{\circ}$ and $\displaystyle 30$ times per minute where the dip is $\displaystyle 60^{\circ}$. The ratio of total magnetic field due to the earth at two places respectively is $\displaystyle \frac{4}{\sqrt{x}}$. The value of $\displaystyle x$ is