Maybe chemistry nerds too. Here's your problem, to settle an argument.

Lets say a person has a quantity of a distilled product. Let's say that distilled product is barrel proofed at 100, or 50% Alcohol by volume (ABV). Said person wants to reduce the proof to 80, or 40%ABV.

How much water would you need to add to a gallon of said distillate to reduce it to 40% ABV?

I am thinking it's not 10%

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