two arcs of concentric circles are intercepted by the same central angle. the resulting arc length of the arc of the larger circle is 16 m and the radius of the smaller circle is 7.5 m. find the length of the corresponding arc of the smaller circle

the complete question in the attached figure

Let
A°-----------> the same central angle

For the larger circle
length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m

360° (full circle) has a length of------------> 75.36 m 
 A°-----------------------------------> 16 m
A°=(16)*360/75.36--------> A=76.43°

For the smaller circle
length of smaller circle=2pi*r-------> 2*pi*7.5-----> 47.1 m

360° (full circle) has a length of------------> 47.1 m 
 76.43°-----------------------------------> X
X=76.43*47.1/360-----> X=10 m ----> length arc of the smaller circle

the answer is
the length arc of the smaller circle is 10 m