3 litres of a mixture containing wine and water in the ratio 3:7 and 4 litres of another mixture containing wine and water in the ratio 3: 5 are mbixed together. What is the ratio of wine and water in the resulting mixture?

Options

A. `11:23`
B. `12:23`
C. `13:24`
D. `12:27`

Answer

To solve the problem of finding the ratio of wine and water in the resulting mixture after combining two mixtures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of Each Mixture:**
- First mixture: 3 liters of wine and water in the ratio 3:7.
- Second mixture: 4 liters of wine and water in the ratio 3:5.

2. **Calculate the Total Parts in Each Mixture:**
- For the first mixture (3:7), the total parts = 3 + 7 = 10 parts.
- For the second mixture (3:5), the total parts = 3 + 5 = 8 parts.

3. **Calculate the Amount of Wine and Water in Each Mixture:**
- For the first mixture:
- Wine = (3/10) * 3 liters = 0.9 liters
- Water = (7/10) * 3 liters = 2.1 liters
- For the second mixture:
- Wine = (3/8) * 4 liters = 1.5 liters
- Water = (5/8) * 4 liters = 2.5 liters

4. **Combine the Amounts of Wine and Water:**
- Total Wine = 0.9 liters (from first mixture) + 1.5 liters (from second mixture) = 2.4 liters
- Total Water = 2.1 liters (from first mixture) + 2.5 liters (from second mixture) = 4.6 liters

5. **Determine the Ratio of Wine to Water in the Resulting Mixture:**
- The ratio of wine to water = Total Wine : Total Water = 2.4 : 4.6
- To simplify this ratio, we can multiply both sides by 10 to eliminate the decimal:
- 2.4 * 10 = 24
- 4.6 * 10 = 46
- Thus, the ratio becomes 24 : 46.

6. **Simplify the Ratio:**
- To simplify 24 : 46, we can divide both numbers by their greatest common divisor (GCD), which is 2:
- 24 ÷ 2 = 12
- 46 ÷ 2 = 23
- Therefore, the simplified ratio of wine to water in the resulting mixture is **12 : 23**.

### Final Answer:
The ratio of wine to water in the resulting mixture is **12 : 23**.

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