CAT (QA) PYQs

Two alcohol solutions, $A$ and $B$, are mixed in the proportion $1:3$ by volume. The volume of the mixture is then doubled by adding solution $A$ such that the resulting mixture has $72 \%$ alcohol. If solution $A$ has $60 \%$ alcohol, then the percentage of alcohol in solution $B$ is

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container 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