Three glasses of sizes 3lt , 4lt and 5lt contains mixture of sprit and water in the ratio` 2 : 3, 3 : 7` and `4 : 11` respectively. All three glasses are poured into a single vessel. Find the ratio of sprit and water in resultant mixture.

Answer

To solve the problem of finding the ratio of spirit and water in the resultant mixture after combining the contents of three glasses, we will follow these steps:

### Step 1: Determine the quantities of spirit and water in each glass.

1. **Glass 1 (3 liters, ratio 2:3)**:
- Total parts = 2 + 3 = 5 parts
- Quantity of spirit = (2/5) * 3 liters = 1.2 liters
- Quantity of water = (3/5) * 3 liters = 1.8 liters

2. **Glass 2 (4 liters, ratio 3:7)**:
- Total parts = 3 + 7 = 10 parts
- Quantity of spirit = (3/10) * 4 liters = 1.2 liters
- Quantity of water = (7/10) * 4 liters = 2.8 liters

3. **Glass 3 (5 liters, ratio 4:11)**:
- Total parts = 4 + 11 = 15 parts
- Quantity of spirit = (4/15) * 5 liters = 1.33 liters (approximately)
- Quantity of water = (11/15) * 5 liters = 3.67 liters (approximately)

### Step 2: Calculate the total quantities of spirit and water.

- **Total Spirit**:
- Total spirit = 1.2 liters (from Glass 1) + 1.2 liters (from Glass 2) + 1.33 liters (from Glass 3)
- Total spirit = 1.2 + 1.2 + 1.33 = 3.73 liters (approximately)

- **Total Water**:
- Total water = 1.8 liters (from Glass 1) + 2.8 liters (from Glass 2) + 3.67 liters (from Glass 3)
- Total water = 1.8 + 2.8 + 3.67 = 8.25 liters (approximately)

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

- The ratio of spirit to water = Total Spirit : Total Water
- Ratio = 3.73 : 8.25

To simplify this ratio, we can convert it into a fraction:
- Ratio = 3.73 / 8.25

Calculating this gives approximately:
- Ratio ≈ 0.452 : 1

To express this in whole numbers, we can multiply both sides by a common factor (for example, 100):
- Ratio ≈ 45.2 : 100

To express it in simplest form, we can round it:
- Ratio ≈ 45 : 100 or approximately 9 : 20 after simplification.

### Final Answer:
The ratio of spirit to water in the resultant mixture is approximately **9 : 20**.

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