Percentage of alcohol after watered down

If you add 1/3 of 40% Vodka to a glass, then add 2/3 orange juice to the glass what would be the overall Alcohol percentage to the glass filled with 2/3 orange juice and 1/3 vodka be?

I was just curious on the question due to bars mixing at a 1/3 ratio, I have horrible math skills therefore I thought this would be the best place to figure it out, thanks :)

40 * (1/3) + 0 * (2/3) = x * (1/3 + 2/3)
40/3 = x
13.3 = x

13.3% alcohol by volume

One third (1/3) of the glass is Vodka.
40% of the Vodka is alcohol.

The amount of alcohol in the glass is therefore 40% of 1/3 of the glass, which is 0.4*(1/3) =

= (4/10)*(1/3) = 4/30 = 2/15 of the glass = amount of alcohol in the glass. You want this as a percentage:

1 glass -------------------------- 100%
2/15 of the glass ------------- x%

x = 100*(2/15) = 200/15 = 13.33% alcohol.

So your answer is 13.33% alcohol.

You can also say arbitrarily that the glass has 100 milliliters of liquid. Therefore, the amount of Vodka (which is 1/3 of the glass) is 100/3 = 33.33 milliliters = amount of Vodka in the glass. Of this amount of Vodka, 40% is alcohol, so the amount of alcohol in the glass is 40% of 33.33 milliliters = 0.4*33.33 milliliters = 13.33 milliliters of alcohol in the glass. Since the glass has 100 milliliters in total liquid, obviously the 13.33 milliliters of alcohol in the glass is 13.33% alcohol.

I hope this helps...

let total volume be = 90 ml
1/3 of 90 = 30 ml
2/3 0f 90 = 60ml
now 30 ml of 40% alcohol = 30 x40/100 = 12 ml alcohol
so overall % of alcohol = 12 x100/90 =120/9
= 13.33 % alcohol ANSWER

13.3% alcohol.

= 100%(1/3[2/5])
= 100%(2/15)
= 200/15% OR 40/3%
= 13 1/3%

Answer: 13 1/3% OR 13.33 1/3%

40%/3 = 13.3%