Average, Mixture and Alligation Question 7 - CAT 2021
The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 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:
Step-by-Step Explanation
Let us analyze this problem using Alligation by tracking the concentration changes in the first bottle.
Initial concentration in Bottle 1 = 33%
Concentration of the solution added from Bottle 2 = 17%
Resulting target mixture concentration = 21%
Set up the alligation cross-subtraction framework:
Bottle 1 (33%) Bottle 2 (17%)
/
/
Resulting (21%)
/
/
|21 − 17| |33 − 21|
= 4 = 12
The ratio of components in the final mixture is:
Ratio = 4 : 12 = 1 : 3
This ratio means that out of a total volume of 1 + 3 = 4 parts inside the first bottle, exactly 3 parts must be drawn from Bottle 2.
Since the first bottle's total capacity is 800 cc:
Volume transferred from Bottle 2 = 3 / 4 × 800 = 600 cc
Since 600 cc of solution was drawn out from Bottle 2 to refill the first bottle, the volume remaining in Bottle 2 is:
Volume Remaining = 800 − 600 = 200 cc
Correct Answer: 200
💡 FundaMakers Tip:
In substitution problems, the mixture ratio found via alligation tells you exactly how much fluid was imported from the external source. Recognizing that a 1:3 ratio requires 600 cc of imported fluid allows you to find the remainder left in Bottle 2 through simple subtraction.