CAT (QA) PYQs

A glass contains $500 \mathrm{cc}$ of milk and a cup contains $500 \mathrm{cc}$ of water. From the glass, $150 \mathrm{cc}$ of milk is transferred to the cup and mixed thoroughly. Next, $150 \mathrm{cc}$ of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture $P$ and replaced with same amount of cocoa powder to form a new mixture $Q$. If the ratio of coffee and cocoa in the mixture $Q$ is $16: 9$, then the ratio of cocoa in mixture $P$ to that in mixture $Q$ 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 $2: 3$?