CAT 2024 Slot 1 · Quant · Question 17

Each operation removes two-thirds of whatever is in the glass, so one-third of the milk survives it.

The volume is restored with water every time, so the glass always holds the same total.

The process runs once and is then repeated three more times, so four operations in all.

After them the milk is {\left( \frac{1}{3}\right)}^{4}=\frac{1}{81} of the original.

The rest of the glass is water, that is \frac{80}{81}.

So milk to water is \frac{1}{81}:\frac{80}{81}.

Clearing the denominators, the ratio is 1:80.

Shortcut. Replacement questions only need the surviving fraction, here \frac{1}{3} per round. Raise it to the number of rounds and the ratio is 1:\left({3}^{4}-1 \right) — note the answer is 1:80, not 1:81, because the second term is water, not the total.