A and B two solutions containing milk nd water. Solution A has 10% milk and B has X% milk. Both are mixed in ratio 3:2 to form a solution C . Then A and C are mixed in equal quantities then milk in resultant solution is 12.5% find X

Let's work through the problem step by step to find the value of \( X \), which represents the percentage of milk in solution B.

### Step 1: Understand the problem
- Solution A has 10% milk.
- Solution B has \( X\% \) milk.
- Solutions A and B are mixed in a ratio of 3:2 to form Solution C.
- Then, solutions A and C are mixed in equal quantities to form the final solution, which has 12.5% milk.

### Step 2: Milk percentage in Solution C
When A and B are mixed in the ratio of 3:2, the milk content in Solution C can be calculated using the weighted average formula for mixtures:

\[
\text{Milk percentage in C} = \frac{3 \times 10\% + 2 \times X\%}{3 + 2}
\]

Simplifying this expression:

\[
\text{Milk percentage in C} = \frac{30 + 2X}{5} = 6 + \frac{2X}{5}
\]

Thus, the milk percentage in Solution C is \( 6 + \frac{2X}{5} \).

### Step 3: Milk percentage in the final mixture
Now, Solution A and Solution C are mixed in equal quantities to form the final solution, which has 12.5% milk. Since they are mixed in equal amounts, the milk percentage in the final solution is the simple average of the milk percentages in Solution A and Solution C:

\[
\frac{10\% + \left(6 + \frac{2X}{5}\right)}{2} = 12.5\%
\]

### Step 4: Set up the equation
We can now set up the equation:

\[
\frac{10 + \left(6 + \frac{2X}{5}\right)}{2} = 12.5
\]

Multiply both sides of the equation by 2 to eliminate the denominator:

\[
10 + 6 + \frac{2X}{5} = 25
\]

Simplify:

\[
16 + \frac{2X}{5} = 25
\]

Subtract 16 from both sides:

\[
\frac{2X}{5} = 9
\]

### Step 5: Solve for \( X \)
Multiply both sides by 5:

\[
2X = 45
\]

Now divide by 2:

\[
X = 22.5
\]

Thus, the percentage of milk in Solution B is \( \boxed{22.5\%} \).

---

Would you like more details or have any questions?

### Related questions:
1. How do you calculate the weighted average in mixtures?
2. What would the final percentage of milk be if Solution B had 25% milk instead of 22.5%?
3. How does changing the mixing ratio of solutions A and B affect the final mixture?
4. What if solutions A and B were mixed in a ratio of 2:3 instead? How would the answer change?
5. Can the formula for weighted averages be used for other substances, like sugar in water?

### Tip:
Always ensure that ratios are applied correctly when mixing solutions to get accurate results in percentage calculations.

A and B two solutions containing milk and water. Solution A has 10% milk and B has X% milk. Both are mixed in ratio 3:2 to form a solution C. Then A and C are mixed in equal quantities, and the milk in the resultant solution is 12.5%. Find X.

Solve a mixture problem where Solution A has 10% milk and Solution B has X% milk. After mixing both in a 3:2 ratio and further combining with Solution A, learn how to find the value of X, ensuring the final mixture has 12.5% milk. Explore key concepts in algebra and weighted averages suitable for Grades 9-12.

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