CAT 2021 Set-1 | Quantitative Aptitude | Question: 11

Question

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100 \; \text{cc}$ of water. Two $800 \; \text{cc}$ 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

Answer 1

We can solve using Allegation and Mixtures method.



The ratio of $\text{Bottle 1 : Bottle 2} = 4:12 = 1:3$

Solution used from $\text{Bottle 2} = \left(\frac{3}{1+3}\right) \times 800 = \frac{3}{4} \times 800 = 3 \times 200 = 600\;\text{cc}$

This amount was added from $\text{Bottle 2}$ into $\text{Bottle 1.}$

$\therefore$ The solution left in $\text{Bottle 2} = 800-600=200\;\text{cc}.$

Correct Answer $:200$