To solve this problem, let's break it down step by step:

Step 1: Define the components of Mixture A and Mixture B.

• Mixture A: The ratio of coffee powder to sugar is $3:2$. So, for every 5 parts of the mixture, 3 parts are coffee powder, and 2 parts are sugar.

  • Percentage of sugar in Mixture A: $\text{Percentage of sugar in A} = \frac{2}{3+2} \times 100 = \frac{2}{5} \times 100 = 40\%$

• Mixture B: The ratio of coffee powder to sugar is $7:3$. So, for every 10 parts of the mixture, 7 parts are coffee powder, and 3 parts are sugar.

  • Percentage of sugar in Mixture B: $\text{Percentage of sugar in B} = \frac{3}{7+3} \times 100 = \frac{3}{10} \times 100 = 30\%$

Step 2: Combine Mixture A and Mixture B in a 2:3 ratio.

Now, Badal Sir combines Mixture A and Mixture B in a $2:3$ ratio.

Let the amount of Mixture A used be $2x$ and Mixture B used be $3x$.

• The sugar content in Mixture A is $40\%$, so the sugar in $2x$ parts of Mixture A is: $\text{Sugar from Mixture A} = 2x \times \frac{40}{100} = 0.8x$

• The sugar content in Mixture B is $30\%$, so the sugar in $3x$ parts of Mixture B is: $\text{Sugar from Mixture B} = 3x \times \frac{30}{100} = 0.9x$

The total amount of mixture is $2x + 3x = 5x$, and the total sugar is $0.8x + 0.9x = 1.7x$.

The percentage of sugar in the combined mixture is: $\text{Percentage of sugar in the combined mixture} = \frac{1.7x}{5x} \times 100 = 34\%$

Step 3: Mix with equal amount of milk.

Now, Badal Sir mixes this combined mixture with an equal amount of milk, which contains no sugar. So, the total amount of the final mixture is doubled, but the sugar content remains the same.

The percentage of sugar in the final mixture is: $\text{Final percentage of sugar} = \frac{1.7x}{2 \times 5x} \times 100 = \frac{1.7}{10} \times 100 = 17\%$

Thus, the percentage of sugar in Badal Sir's final mixture is 17%.

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Would you like further clarification or details on any step?

Here are 5 related questions to deepen your understanding:

1. What is the percentage of coffee powder in Badal Sir's final mixture?
2. If Badal Sir used 1 liter of milk, how much sugar is present in the final drink?
3. What would happen if Mixture A and Mixture B were combined in a 1:1 ratio?
4. How would the sugar percentage change if the final mixture included 50% more milk?
5. How much coffee powder is present in the final mixture?

Tip: When solving ratio problems, break them down step-by-step and ensure each mixture is treated separately before combining them.