BTGModeratorVI wrote: ↑

Wed Jan 06, 2021 8:18 am

A 400 milliliter solution is 20% alcohol by volume. If 100 milliliters of water is added, what is the new concentration of alcohol, as a percent of volume?

(A) 5%
(B) 10%
(C) 12%
(D) 12.5%
(E) 16%

Answer: E

Solution:

If a 400-milliliter solution is 20% alcohol by volume, it has 400 x 0.2 = 80 milliliters of alcohol. Thus the concentration of alcohol, when 100 milliliters of water is added, is:

80 / (400 + 100) = 80/500 = 16/100 = 16%

Alternate Solution:

To a 400 ml solution of 20% alcohol, we add 100 ml of water, which has 0% alcohol, and we obtain 500 ml of a solution with x% alcohol. Creating an equation, we have:

400 (0.20) + 100 (0) = 500x

80 + 0 = 500x

0.16 = x

Converted to a percent, we see that x = 16%.


Answer: E

BTGModeratorVI wrote: ↑

Wed Jan 06, 2021 8:18 am

A 400 milliliter solution is 20% alcohol by volume. If 100 milliliters of water is added, what is the new concentration of alcohol, as a percent of volume?

(A) 5%
(B) 10%
(C) 12%
(D) 12.5%
(E) 16%

Answer: E
Source: Manhattan prep

A 400 milliliter solution is 20% alcohol by volume.
20% of 400 = 80
So, the original solution contains 80 milliliters of alcohol

If 100 milliliters of water is added...
400 + 100 = 500
So, our NEW solution has a total volume of 500 milliliters

...what is the new concentration of alcohol, as a percent of volume?
NEW concentration of alcohol = 80/500
Divide top and bottom of our fraction by 5 to get: 16/100, which is the same as 16%

Answer: E

Cheers,
Brent