Average, Mixture and Alligation Question 2 - CAT 2023
Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be:
Step-by-Step Explanation
Choose a smart total volume for the mixtures to eliminate working with fractions.
- Let the volume of Mixture A be 200 ml.
- Let the volume of Mixture B be 300 ml.
(This perfectly satisfies the specified blending ratio of 2 : 3)
- Calculate the Sugar content:
In Mixture A: Sugar is part of a 3 : 2 cocoa to sugar ratio.
Sugar in A = 2 / (3 + 2) × 200 = 2 / 5 × 200 = 80 ml
In Mixture B: Sugar is part of a 7 : 3 coffee to sugar ratio.
Sugar in B = 3 / (7 + 3) × 300 = 3 / 10 × 300 = 90 ml
- Analyze the Final Drink Mixture:
When combined to form Mixture C:
Total Volume of C = 200 + 300 = 500 ml
Total Sugar in C = 80 + 90 = 170 ml
Mixture C is then combined with an equal amount of milk (500 ml) to create the final drink:
Total Drink Volume = 500 + 500 = 1000 ml
Percentage of Sugar = 170 / 1000 × 100% = 17%
Correct Option: A
💡 FundaMakers Tip:
When the problem combines a specific volume ratio (2 : 3) with fractional component breakdowns (like fifths and tenths), pick a base common multiple like 200 and 300 instead of 2 and 3. This keeps your calculations focused on clean integers and entirely eliminates fractions.