CAT (QA) PYQs

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 $2: 3$?

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

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100 \mathrm{cc}$ of water. Two $800 \mathrm{cc}$ bottles are filled with indigo solutions of strengths $33 \%$ and $17 \%$, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to $21 \%$ then the volume, in cc, of the solution left in the second bottle is