Three utensils contain equal quantity of mixtures of milk and water in the ratio 6:1, 5:2 and 3: 1 respectively. If all the solutions are mixed together, the ratio of milk and water in the final mixture is

Options

A. `65:28`
B. `65:19`
C. `19:65`
D. `19:28`

Answer

To solve the problem of finding the final ratio of milk and water when mixing three mixtures with different ratios, we can follow these steps:

### Step 1: Understand the Ratios
We have three utensils with the following ratios of milk to water:
- Utensil 1: Milk : Water = 6 : 1
- Utensil 2: Milk : Water = 5 : 2
- Utensil 3: Milk : Water = 3 : 1

### Step 2: Calculate the Total Parts in Each Mixture
For each utensil, we calculate the total parts of the mixture:
- Utensil 1: 6 + 1 = 7 parts
- Utensil 2: 5 + 2 = 7 parts
- Utensil 3: 3 + 1 = 4 parts

### Step 3: Calculate the Quantity of Milk and Water
Assuming each utensil contains an equal quantity of the mixture (let's say 7 liters for simplicity), we can calculate the quantities of milk and water in each utensil.

**Utensil 1:**
- Milk = (6/7) * 7 = 6 liters
- Water = (1/7) * 7 = 1 liter

**Utensil 2:**
- Milk = (5/7) * 7 = 5 liters
- Water = (2/7) * 7 = 2 liters

**Utensil 3:**
- Milk = (3/4) * 7 = 5.25 liters
- Water = (1/4) * 7 = 1.75 liters

### Step 4: Sum the Quantities of Milk and Water
Now we sum the quantities of milk and water from all three utensils:

**Total Milk:**
- Utensil 1: 6 liters
- Utensil 2: 5 liters
- Utensil 3: 5.25 liters

Total Milk = 6 + 5 + 5.25 = 16.25 liters

**Total Water:**
- Utensil 1: 1 liter
- Utensil 2: 2 liters
- Utensil 3: 1.75 liters

Total Water = 1 + 2 + 1.75 = 4.75 liters

### Step 5: Find the Final Ratio
Now we can find the ratio of milk to water in the final mixture:
- Ratio of Milk : Water = Total Milk : Total Water = 16.25 : 4.75

To simplify this ratio, we can divide both sides by 4.75:
- Milk : Water = 16.25 / 4.75 : 4.75 / 4.75 = 3.42 : 1

To express it in a simpler form, we can multiply both sides by 100 to avoid decimals:
- Milk : Water = 342 : 100

### Final Answer
The final ratio of milk to water in the mixture is approximately **342 : 100**.