Many people did this one correctly. First one to send the right answer was Ashish Gupta, my colleague at Helion. Also got correct answer from Pooja Goyal and Anirudh Baddepudi.
Many people typically attempt this problem by doing a series, i.e. first person drinks 1/2, second one drinks 1/4, then the first one drinks 1/8 again, etc. While that can help you come at a series and one can use algebra to arrive at the right answer, the simpler way to think about the problem is the following – in each set of one chance each by the two people, “I” drinks twice of “You” (1/2 and 1/4 respectively in the first chance, and 1/8 and 1/16 respectively in the second chance, etc.), and therefore that will hold true for the overall pint of juice. “I” will therefore drink 2/3 and “You” will drink 1/3.
Ashish also solved it without resorting to Algebra where he put the two series on top of each other and realized that one is twice of the other, and arriving at the same answer.
Hope you enjoyed the puzzle!
Alok Goyal's Puzzles Page 
I loved this puzzle and shared it with my family on Mother’s Day. One of my sons teasingly asked me why I needed an answer…Was it because the orange juice was poisonous and the exact amount of antidote needed to be calculated??