Red and Blue paint problem

Q:If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it
mathematically.

A: let the initial red and blue paint be V1, the cup size be Vc, and assume the bucket size Vb>V1+Vc, V1>>Vc, and the two paints are distributed uniformly in red bucket after the first pouring.
in red bucket, the ratio of red and blue is Rr = V1/Vc,
in blue bucket, the ration of blue and red is
Rb = ((V1-Vc) + Vc * Vc/(Vc+V1)) / (Vc*V1/(Vc+V1))
= V1/Vc
So the two buckets have the same ratio.