After 1 spoon beer is added to water, vessel 1 contains V parts of water and v parts of beer.
After 1 spoon mixture is added to beer, vessel 2 contains V-v parts of beer and v parts of (beer+water in the ratio v:V).
Parts of beer contained in vessel 2 =
Parts of water contained in vessel 2=
The ratio is
So, both the liquids are equally pure.