AHSME 1968 Problem 11

If an arc of $60^{\circ}$ on circle $I$ has the same length as an arc of $45^{\circ}$ on circle $II$, the ratio of the area of circle $I$ to that of circle $II$ is: $\text{(A) } 16:9 \text{(B) } 9:16 \text{(C) } 4:3 \text{(D) } 3:4 \text{(E) } \text{none of these}$