If a 19-cup mixture of powder and water contained 1 cup of p

Check out this post for a discussion on mixtures and the responses below it discuss exactly these type of questions in detail: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/04 ... -mixtures/

For me, the most intuitive response here would be this (as done by Mike): Since 19 cups of mix has 1 cup powder, it will have 18 cups water. Now you add powder to make the ratio 1:2 which means that for the 18 cups of water, you must have 9 cups of powder. You already have 1 cup so you add another 8 cups of water.

You can also us the standard weighted average concept to solve such questions in case the given numbers are not so pliable.

Concentration of powder in Mix 1 = 1/19
Concentration of powder in Mix 2 = 1 ( i.e. 100% since it is all powder)
Concentration of powder in final mixture = 1/3

w1/w2 = (1 - 1/3)/(1/3 - 1/19) = 19/8

So for every 19 cups of mix1, you need to put 8 cups of powder to make the required mix with ratio 1:2.

Plug in numbers

Info given Current ratio of powder to water is 1:18 (19 cups total)
We need the ration to be 1:2

Start with statement B we add 8 cups of water now we 9:18 or 1:2

So answer B

Initially
Powder: water = 1:18
To make the ratio 1:2 we need 8 cups of powder to make 9 cup powder and 18 cup water.
Option B

Initially
Powder: water = 1:18
To make the ratio 1:2 or 9:18
we need 8 cups of powder to make 9 cup powder and 18 cup water.

Let x cups of powder be added, so new ratio is

(1+x)/18 = 1/2
Simplifying x = 8
B is correct.