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 $20 \%$ ethanol solution is mixed with another ethanol solution, say, $S$ of unknown concentration in the proportion $1:3$ by volume. This mixture is then mixed with an equal volume of $20 \%$ ethanol solution. If the resultant mixture is a $31.25 \%$ ethanol solution, then the unknown concentration of $S$ 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 $2: 3$?