Three bottles of equal capacity contain mixture of milk and wa ter in ratio 2:3, 3:5 and 4:5 respectively. These three bottles are emptled into a large bottle. What is the ratio of milk and wa ter respectively in the large bottle?

Options

A. `439:1080`
B. `439:641`
C. `439:360`
D. `439:79`

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 will follow these steps:

### Step 1: Define the Ratios and Calculate the Total Parts
1. **Bottle 1** has a milk to water ratio of 2:3. This means for every 5 parts of the mixture, 2 parts are milk and 3 parts are water.
2. **Bottle 2** has a milk to water ratio of 3:5. This means for every 8 parts of the mixture, 3 parts are milk and 5 parts are water.
3. **Bottle 3** has a milk to water ratio of 4:5. This means for every 9 parts of the mixture, 4 parts are milk and 5 parts are water.

### Step 2: Assume Equal Capacity for Each Bottle
Assume each bottle has a capacity of 1 liter. Therefore, the total volume of each bottle is 1 liter.

### Step 3: Calculate the Amount of Milk and Water in Each Bottle
1. **Bottle 1**:
- Milk = (2/5) * 1 liter = 0.4 liters
- Water = (3/5) * 1 liter = 0.6 liters

2. **Bottle 2**:
- Milk = (3/8) * 1 liter = 0.375 liters
- Water = (5/8) * 1 liter = 0.625 liters

3. **Bottle 3**:
- Milk = (4/9) * 1 liter = 0.444 liters (approximately)
- Water = (5/9) * 1 liter = 0.556 liters (approximately)

### Step 4: Sum the Amounts of Milk and Water
Now, we will sum the amounts of milk and water from all three bottles.

- **Total Milk**:
- From Bottle 1: 0.4 liters
- From Bottle 2: 0.375 liters
- From Bottle 3: 0.444 liters
- Total Milk = 0.4 + 0.375 + 0.444 = 1.219 liters (approximately)

- **Total Water**:
- From Bottle 1: 0.6 liters
- From Bottle 2: 0.625 liters
- From Bottle 3: 0.556 liters
- Total Water = 0.6 + 0.625 + 0.556 = 1.781 liters (approximately)

### Step 5: Calculate the Ratio of Milk to Water
Now, we will calculate the ratio of milk to water in the large bottle.

- Ratio of Milk to Water = Total Milk : Total Water
- Ratio = 1.219 : 1.781

To simplify this ratio, we can multiply both sides by a common factor to eliminate the decimals.

### Step 6: Simplifying the Ratio
To simplify the ratio, we can convert it into whole numbers:
- Multiply both sides by 1000 (to remove decimals):
- Milk = 1219
- Water = 1781

Thus, the ratio of milk to water in the large bottle is approximately **1219 : 1781**.

### Final Answer
The ratio of milk to water in the large bottle is approximately **1219 : 1781**.

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