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To solve this problem, we need to find the concentration of milk in the new mixture after mixing the contents of vessels \(X\) and \(Y\).

### Step-by-Step Solution:

1. **Milk Concentration in Each Vessel:**
   - Vessel \(X\) contains 80% milk.
   - Vessel \(Y\) contains 50% milk.

2. **Mixing Ratio:**
   The contents are mixed in the ratio \(3:2\). This means that for every 3 parts of vessel \(X\), there are 2 parts of vessel \(Y\).

3. **Calculate the Weighted Average Concentration:**
   We use the weighted average formula for the concentration of milk:
   \[
   \text{Concentration} = \frac{(3 \times 80) + (2 \times 50)}{3 + 2}
   \]
   Here:
   - \(3 \times 80 = 240\) (contribution of vessel \(X\))
   - \(2 \times 50 = 100\) (contribution of vessel \(Y\))

4. **Perform the Calculation:**
   \[
   \text{Concentration} = \frac{240 + 100}{5} = \frac{340}{5} = 68\%
   \]

Therefore, the concentration of milk in the new mixture is **68%**.

Would you like more details on this or have any questions?

### Related Questions:
1. How would the concentration change if vessel \(Y\) had a different milk percentage?
2. What happens to the concentration if the mixing ratio is altered, say to \(1:1\)?
3. How can the formula for weighted averages be used in other scenarios, like test scores?
4. What is the effect of adding more water to the final mixture?
5. How would you calculate the concentration if vessel \(X\) had a higher milk percentage, say 90%?

### Tip:
To solve mixture problems efficiently, always remember to use the weighted average formula, considering the given ratios and concentrations.

A vessel 'X' contains liquid having 80% milk. Another vessel 'Y' contains a liquid having 50% milk. The contents of the two vessels are mixed in a ratio of 3:2 in another big container. What is the concentration of milk in this container?

Solve the mixture problem where a vessel with 80% milk and another with 50% milk are combined in a 3:2 ratio. Learn how to calculate the concentration of milk in the final mixture using the weighted average formula. Suitable for Grades 6-8.

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