Wira has 2 bottles, $A$ and $B$.
Initially:
bottle $A$ is $3/4$ pure water and $1/4$ empty
bottle $B$ is $3/4$ milk and $1/4$ empty
Wira then pours from $A$ to $B$ until $B$ is full. Then $B$ is shaken until the mixture is even. After that, $B$ is poured to $A$ until it $A$ is full. Now, what is the ratio of pure water and milk in $A$?
Attempt:
Let the size of $A$ be $a$, the size of $B$ be $b$.
So initially there is 100% water in $A$, but the amount is $3a/4$. Simlarly 100% milk in $B$, with amount $3b/4$. After pouring from $A$ to $B$,
$$ B:= \frac{3}{4}b \text{ milk, } \frac{1}{4}b \text{ pure water} $$
$$ A := 0\% \text{ milk, } \frac{3}{4}a - \frac{1}{4}b \text{ pure water}$$
Now, there are $\frac{1}{4}a + \frac{1}{4}b$ of space left in $A$. After $B$ (with even mixture) is then poured to $A$, $A$ will have additional $\frac{3}{4} \left( \frac{1}{4}a + \frac{1}{4}b \right)$ of milk, and $\frac{1}{4} \left( \frac{1}{4}a + \frac{1}{4}b \right)$ of pure water.
$$ A := \frac{3}{4} \left( \frac{1}{4}a + \frac{1}{4}b \right) \text{ milk, } \frac{3}{4}a - \frac{1}{4}b + \frac{1}{4} \left( \frac{1}{4}a + \frac{1}{4}b \right) \text{ pure water}$$
So.. the problem does not state the size of each bottle, and I cannot answer about the ratio without knowing the size of each bottle. Is this true?
Assuming they are the same size, so the ratio is $5:3$.
Your approach to the problem is correct and you have the right answer.
The volumes of the bottle do matter in this question and they will certainly affect the answer. This is because the volume determines how much fluid is required before is becomes full. Hence the answer can only be simplified to an equation where one has to substitute the volumes.
Tip: When in doubt in such questions, take the total to be 100. Absolutes are easier to work with as compared to fractions.