Let r1,r2 and θ1,θ2 be the radii and angles subtended at the centreof two circles respectively.
So, θ1 = 60° = (

π

180

×60) radians =

π

3

radians [Since 1° = π/180 radians]
and θ2 = 60° = (

π

180

×75) radians =

5π

12

radians
Let l be the length of the arc, then, l = r1θ1 and l = r2θ2
⇒ r1θ1 = r2θ2 ⇒

r1

r2

=

5π

12

×

3

π

=

5

4

Hence, the required ratio is 5 : 4.