If the arcs of the same length in two circles subtend angles

Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$

$\theta=\frac{1}{r}$ where $\theta$ is central angle, $l=$ length of arc, $r=$ radius

Therefore $\theta_{1}=75 \times \frac{\pi}{180}=\frac{5 \pi}{12}$

$\theta_{2}=120 \times \frac{\pi}{180}=\frac{2 \pi}{3}$

$I=r \times \theta$

Now, as the length is the same

Therefore, $r_{1} \times \theta_{1}=r_{2} \times \theta_{2}$

$r_{1} \times \frac{5 \pi}{12}=r_{2} \times \frac{2 \pi}{3}$

$\frac{r_{1}}{r_{2}}=\frac{12}{5 \pi} \times \frac{2 \pi}{3}=\frac{24}{15}=\frac{8}{5}$

Therefore the ratio of their radii is 8 : 5