CAT (QA) PYQs

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

A solution, of volume $40$ litres, has dye and water in the proportion $2: 3$. Water is added to the solution to change this proportion to $2: 5$. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to $2: 3$?

A chemist mixes two liquids $1$ and $2$. One litre of liquid $1$ weighs $1 \mathrm{~kg}$ and one litre of liquid $2$ weighs $800 \mathrm{gm}$. If half litre of the mixture weighs $480 \mathrm{gm}$, then the percentage of liquid $1$ in the mixture, in terms of volume, is