Three jugs of equal capacity are filled with mixtures of milk and water in the proportions 3:1, 7: 1 and 11: 5. The three jugs are emptied into a single container. What will be the ratio of water to milk in the said container?

Options

A. `14:45`
B. `11:37`
C. `12:41`
D. `15:49`

Answer

To solve the problem, we need to find the total amount of milk and water in the three jugs and then determine the ratio of water to milk in the combined mixture.

### Step-by-Step Solution:

1. **Identify the proportions of milk and water in each jug:**
- Jug 1: Milk to Water = 3:1
- Jug 2: Milk to Water = 7:1
- Jug 3: Milk to Water = 11:5

2. **Assume a common capacity for each jug:**
Let's assume each jug has a capacity of 1 liter for simplicity.

3. **Calculate the total parts in each jug:**
- Jug 1: Total parts = 3 + 1 = 4 parts
- Jug 2: Total parts = 7 + 1 = 8 parts
- Jug 3: Total parts = 11 + 5 = 16 parts

4. **Calculate the volume of milk and water in each jug:**
- Jug 1:
- Milk = (3/4) * 1 liter = 0.75 liters
- Water = (1/4) * 1 liter = 0.25 liters
- Jug 2:
- Milk = (7/8) * 1 liter = 0.875 liters
- Water = (1/8) * 1 liter = 0.125 liters
- Jug 3:
- Milk = (11/16) * 1 liter = 0.6875 liters
- Water = (5/16) * 1 liter = 0.3125 liters

5. **Sum the total volumes of milk and water:**
- Total Milk = 0.75 + 0.875 + 0.6875 = 2.3125 liters
- Total Water = 0.25 + 0.125 + 0.3125 = 0.6875 liters

6. **Calculate the ratio of water to milk:**
- Ratio of Water to Milk = Total Water : Total Milk = 0.6875 : 2.3125
- To simplify, we can multiply both sides by 16 (to eliminate the decimals):
- Water = 0.6875 * 16 = 11
- Milk = 2.3125 * 16 = 37
- Therefore, the ratio of water to milk = 11 : 37.

### Final Answer:
The ratio of water to milk in the container is **11 : 37**.