CAT 2023Slot 3QAQuestion & Solution
Question
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
Options
17
16
21
24
Solution
1. Concept Used
- Topic: Ratio and Proportion — Mixture Problems
- Formula: $$\text{Percentage of Sugar} = \frac{\text{Total Sugar in Final Drink}}{\text{Total Volume of Final Drink}} \times 100$$
2. Calculation
To solve this problem cleanly, assign convenient volumes that respect all the given ratios simultaneously.
Mixture A (Cocoa : Sugar = 3 : 2): Since A and B are combined in the ratio 2 : 3, let the volume of Mixture A be 200 ml. This gives: $$\text{Cocoa in A} = \frac{3}{5} \times 200 = 120 \text{ ml}, \quad \text{Sugar in A} = \frac{2}{5} \times 200 = 80 \text{ ml}$$
Mixture B (Coffee : Sugar = 7 : 3): Correspondingly, let the volume of Mixture B be 300 ml. This gives: $$\text{Coffee in B} = \frac{7}{10} \times 300 = 210 \text{ ml}, \quad \text{Sugar in B} = \frac{3}{10} \times 300 = 90 \text{ ml}$$
Mixture C is formed by combining A and B in the ratio 2 : 3 (200 ml : 300 ml): $$\text{Total volume of C} = 200 + 300 = 500 \text{ ml}$$ $$\text{Total sugar in C} = 80 + 90 = 170 \text{ ml}$$
Final Drink: Mixture C is mixed with an equal amount of milk, so 500 ml of milk is added: $$\text{Total volume of drink} = 500 + 500 = 1000 \text{ ml}$$
The sugar content does not change (milk contains no sugar), so: $$\text{Percentage of sugar} = \frac{170}{1000} \times 100 = 17%$$
3. Solution
Answer = Option A ✅
The percentage of sugar in the final drink is 17%.