Question

In mixture A, the ratio of coco and sugar is 3:2 and in mixture B, the ratio of coffee and sugar is 7 : 3. These two were mixed together in the ratio 2:3 to make mixture C. Now equal quantities of C and milk are mixed. Find the percentage of sugar in the mixture.

Answer 1

Approach: Pick convenient amounts that respect the $2:3$ mixing ratio, total the sugar, then halve for the final milk dilution.

Step 1: In mixture A, sugar is $\frac{2}{3+2}=\frac{2}{5}$ of the whole; in mixture B, sugar is $\frac{3}{7+3}=\frac{3}{10}$ of the whole.

Step 2: Take $2$ litres of A and $3$ litres of B (ratio $2:3$), giving $5$ litres of C. Sugar $=2\times\frac25+3\times\frac3{10}=0.8+0.9=1.7$ litres.

Step 3: So C is $\frac{1.7}{5}=34\%$ sugar.

Step 4: Mixing equal quantities of C with sugar-free milk halves the concentration: $\frac{34\%}{2}=17\%$.

Answer: The final mixture is $17\%$ sugar.