smc

Suppose that the constant is $x$. Then $20+x,50+x,100+x$ is a geometric progression, so $(20+x)(100+x)=(50+x{)}^2$. Expanding, we get $2000+120x+x^2=2500+100x+x^2$; therefore, $20x=500$, so $x=25$. Now we can calculate our geometric progression to be $20+25,50+25,100+25=45,75,125$. Therefore, the common ratio is $\frac{125}{75}=\frac{75}{45}=\boxed{\frac{5}{3}}$, and our answer is $\boxed{\frac{5}{3}}$.