arc length

As we know that, $l=r\theta$ .
For Circle 1, $l_1=r_1 \theta_1\rightarrow Eq.1$
For Circle 2, $l_2=r_2 \theta_2\rightarrow Eq.2$
Dividing $Eq.1$ by $Eq.2$ , we get,
$\frac{l_1}{l_2} = \frac{r_1\theta_1}{r_2\theta_2}$
$\Rightarrow \frac{r_1}{r_2}= \frac{l_1\theta_2}{l_2\theta_1}$
Since, $l_1=l_2$ ,
$\Rightarrow \frac{r_1}{r_2}= \frac{\theta_2}{\theta_1}$
$\Rightarrow \frac{r_1}{r_2}= \frac{75}{60}$
So, $\frac{r_1}{r_2}=\frac{5}{4}$
Hence, $r_1:r_2=5:4$ .

Since they have equal arc length, the ratio of their radii is the ratio of their central angles. We have

$\dfrac{R}{r}=\dfrac{75}{60}=\dfrac{5}{4}$

Actually the answer should be 4:5.........As the angle 60 degree which is smaller is given earlier than the bigger one.....