Three bottles of equal capacity are containing a mixture of milk and water in ratio 2: 1, 3:7 and 4: 11 respectively. These three bottles are emptied into a large bottle. What is the ratio of milk and water respectively in this large bottle?

Options

A. `37:53`
B. `37:90`
C. `37:30`
D. `7:30`

Answer

To solve the problem of finding the ratio of milk and water in the large bottle after mixing the contents of the three smaller bottles, we can follow these steps:

### Step 1: Understand the Ratios
The three bottles contain mixtures of milk and water in the following ratios:
- Bottle 1: Milk : Water = 2 : 1
- Bottle 2: Milk : Water = 3 : 7
- Bottle 3: Milk : Water = 4 : 11

### Step 2: Determine Total Parts in Each Bottle
For each bottle, we can find the total parts of the mixture:
- Bottle 1: 2 + 1 = 3 parts
- Bottle 2: 3 + 7 = 10 parts
- Bottle 3: 4 + 11 = 15 parts

### Step 3: Calculate the Amount of Milk and Water
Assuming each bottle has a capacity of 30 liters (the LCM of the total parts), we can calculate the amount of milk and water in each bottle.

- **Bottle 1:**
- Milk = (2/3) * 30 = 20 liters
- Water = (1/3) * 30 = 10 liters

- **Bottle 2:**
- Milk = (3/10) * 30 = 9 liters
- Water = (7/10) * 30 = 21 liters

- **Bottle 3:**
- Milk = (4/15) * 30 = 8 liters
- Water = (11/15) * 30 = 22 liters

### Step 4: Sum Up the Milk and Water
Now, we will sum up the total amount of milk and water from all three bottles.

- **Total Milk:**
- From Bottle 1: 20 liters
- From Bottle 2: 9 liters
- From Bottle 3: 8 liters
- Total Milk = 20 + 9 + 8 = 37 liters

- **Total Water:**
- From Bottle 1: 10 liters
- From Bottle 2: 21 liters
- From Bottle 3: 22 liters
- Total Water = 10 + 21 + 22 = 53 liters

### Step 5: Find the Final Ratio
Now, we can find the ratio of milk to water in the large bottle:
- Ratio of Milk : Water = 37 : 53

### Final Answer
The ratio of milk and water in the large bottle is **37 : 53**.

---