My solution:

Notice: "half alcohol/half water" means solution with 50% concentration.
Let x be the amount of the 25% solution and y the amount of the 50% solution.

Using aligation:

X Y
I----------------I-----------------I
0.25-------------0.3-------------0.5

x/y = 0.2/0.05 = 20/5 =4 so x = 4y.

Amount of the solution = y + x = y + 4y = 5y.
Percentage of the original alcohol replaced = part replaced/Amount of the solution = 4y/5y = 0.8 = 80%

First of all, l love question like this. Thanks Bunuel!
let x be the total volume of the original mixture of half alcohol and half water
let y be the portion that was removed from the mixture x
We must have in mind that the volume of the portion(y) removed is equal to the volume of solution that replaced it
Hence, % of alcohol in final solution =(0.5x - 0.5y + 0.25y)/(x - y + y) =30%
(0.5x - 0.25y)/(x) =0.3
0.5x - 0.25y =0.3x
0.2x =0.25y
y = 0.8x
or 80% of original mixture

Refer to Graph attached:

If the mixture was replaced with an equal amount of the 25% alcohol solution, it should result in a 37.5% alcohol solution instead of 30% alcohol solution.
--This means that more than 50% of the original solution was replaced with the 25% solution. Eliminate A and B

If you subtract the differences, you get a ratio of 5x:20x => 1x:4x = 5x
--That means, for every 5 liters (1x+4x), you have 1 part of 50% alcohol solution and 4 parts of the 25% solution

4:5 = 80%

Answer E

I think this the explanation isn't clear enough, please elaborate.