Three glasses of capacity 2 lt , 5 ltand 9 ltcontain mixture of milk and water with milk concentrations `90%, 80% `and `70%` respectively. The contents of three glasses are emptied into a large vessel. Find the ratio of milk and water in the resultant mixture .

Answer

To solve the problem, we will calculate the total amount of milk and water in the mixture from the three glasses and then find the ratio of milk to water.

### Step 1: Calculate the amount of milk and water in each glass.

**Glass A (2 liters, 90% milk):**
- Milk = 90% of 2 liters = \(0.90 \times 2 = 1.8\) liters
- Water = 10% of 2 liters = \(0.10 \times 2 = 0.2\) liters

**Glass B (5 liters, 80% milk):**
- Milk = 80% of 5 liters = \(0.80 \times 5 = 4\) liters
- Water = 20% of 5 liters = \(0.20 \times 5 = 1\) liter

**Glass C (9 liters, 70% milk):**
- Milk = 70% of 9 liters = \(0.70 \times 9 = 6.3\) liters
- Water = 30% of 9 liters = \(0.30 \times 9 = 2.7\) liters

### Step 2: Sum the amounts of milk and water from all glasses.

**Total Milk:**
- From Glass A: 1.8 liters
- From Glass B: 4 liters
- From Glass C: 6.3 liters

Total Milk = \(1.8 + 4 + 6.3 = 12.1\) liters

**Total Water:**
- From Glass A: 0.2 liters
- From Glass B: 1 liter
- From Glass C: 2.7 liters

Total Water = \(0.2 + 1 + 2.7 = 3.9\) liters

### Step 3: Find the ratio of milk to water.

The ratio of milk to water is given by:

\[ \text{Ratio} = \frac{\text{Total Milk}}{\text{Total Water}} = \frac{12.1}{3.9} \]

To simplify this ratio, we can divide both the numerator and denominator by 3.9:

\[ \frac{12.1 \div 3.9}{3.9 \div 3.9} = \frac{3.1}{1} \]

Thus, the ratio of milk to water in the resultant mixture is:

\[ \text{Ratio of Milk to Water} = 3.1 : 1 \]

### Final Answer:
The ratio of milk to water in the resultant mixture is \(3.1 : 1\).

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