When two sprockets are in contact with each other then at the contact of sprockets the tangential velocity and tangential acceleration of the sprockets must be same.
Now we can say that tangential velocity is given as
v = Rw
here we know that
[tex]w = 2\pi f[/tex]
also we can say
[tex]2\pi R = N*x[/tex]
x = width of each sprocket
So tangential speed is given as
[tex]v = \frac{N*x}{2\pi} * 2\pi f[/tex]
now since tangential speed of two sprockets are same
[tex] N_1*x*f_1 = N_2*x*f_2[/tex]
given that
[tex]N_1[/tex] = 50
[tex]f_1[/tex] = 20 rpm
[tex]N_2[/tex] = 30
now from above equation
[tex]50*20 = f_2 * 30[/tex]
[tex]f_2 = \frac{100}{3}[/tex] rpm
