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

CAT 2023 Slot 3 QA Question 8

Multiple choice (+3 / −1) · Arithmetic · Mixture & Alligation · Try it, then check the answer and solution below.

CAT 2023 Slot 3QAArithmetic • Mixture & AlligationEasy

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

. He combines mixtures

and

in the ratio

2: 3

to make a new mixture

. If he mixes

C$ with an equal amount of milk to make a drink, then the percentage of sugar in this drink will

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Official Convenor Answer Key: A

Answer and solution

Answer: A) $17$

📌 Core Concept

The problem involves multiple stages of mixture preparation and combination. The key concept is to calculate the percentage of sugar in each mixture step-by-step and then determine the final percentage after combining with milk.

🔢 Step-by-Step Solution

Calculate Sugar Percentage in Mixture A:

Ratio of cocoa to sugar:

3:2

Total parts = 3 + 2 = 5$

Sugar percentage in A:

\frac{2}{5} \times 100 = 40\%

Calculate Sugar Percentage in Mixture B:

Ratio of coffee to sugar:

7:3

Total parts = 7 + 3 = 10$

Sugar percentage in B:

\frac{3}{10} \times 100 = 30\%

Calculate Sugar Percentage in Mixture C:

Ratio of A to B:

2:3

Sugar in C:

\frac{2 \times 40\% + 3 \times 30\%}{2 + 3} = \frac{80\% + 90\%}{5} = \frac{170\%}{5} = 34\%

Mix Mixture C with Milk:

Equal amount of milk (0% sugar) is added.

Let the amount of C be

x

. Then, milk added is also

x

Total mixture:

x + x = 2x

Sugar in drink:

34\% \text{ of } x = 0.34x

Sugar percentage in drink:

\frac{0.34x}{2x} \times 100 = \frac{0.34}{2} \times 100 = 17\%

⚡ 30-Second Shortcut

Calculate sugar percentages for A and B: 40% and 30%.

Use weighted average

CAT 2023 Slot 3 QA Question 8

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