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

The strength of a salt solution is $\mathrm{p} \%$ if $100 \mathrm{ml}$ of the solution contains $p$ grams of salt. Each of three vessels $\mathrm{A}, \mathrm{B}, \mathrm{C}$ contains $500 \mathrm{ml}$ of salt solution of strengths $10 \%, 22 \%$, and $32 \%$, respectively. Now, $100 \mathrm{ml}$ of the solution in vessel A is transferred to vessel B. Then, $100 \mathrm{ml}$ of the solution in vessel $B$ is transferred to vessel $C$. Finally, $100 \mathrm{ml}$ of the solution in vessel $C$ is transferred to vessel $A$. The strength, in percentage, of the resulting solution in vessel $A$ is