Problem on comparision of radii

Question

The radius of one circle is $4$ times that of a second. Compare an arc subtending $45°$ at the centre of the first with one subtending $60°$ at the centre of second.

I understood the first part of the question But the second condition confused me.

Answer 1

Arc length is proportional to the angle subtended. For example, an arc subtending $90°$ is twice as long as an arc subtending $45°$. Arc length is also proportional to the radius of the circle, so an arc in a circle of radius $2$ will be twice as long as an arc subtending the same angle in a circle of radius $1$.

We can multiply these proportions; the arc in your second circle is $$\frac{\theta_2}{\theta_1}\cdot\frac{r_2}{r_1}=\frac{60°}{45°}\cdot\frac41=\frac{16}3$$ times as long as the first.