Problem Solving

This concept has yet to make sense to me (alligation i think its called), but it yields the correct answer. Can someone offer up a Barney-style explanation of this concept?

From "Tough Gmat math problems"

7. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) ¾

My solution:

x = 40%, y = 25%, new formula "z" = 35%.

Proportion of X = |25-35| = 10
Proportion of Y = |40-35| = 5

X to Y is therefore 10 to 5. IOW, X = 2/3 of the new formula z. Therefore 1/3 of X was replaced by Y.

OA: [spoiler]1/3rd[/spoiler]

The allegation method is the easiest to do such problems.

One other way of doing it,
This could be considered as a weighted Avg question

40x + 25y / (x+y) = 35 (X quantity of 40% and y of 25% are mixed to form 35%)

Solving you get 5x=10y.

Same as you found using allegations

check for explanation by Mitch,

https://www.beatthegmat.com/difficult-ma ... -t455.html