There are three containers of equal capacity. The ratio of Sulphuric acid to water in the first container is 3: 2, that in the second container is 7:3 and in the third container it is 11:4. If all the liquids are mixed together, then the ratio of Sulphuric acid to water in the mixture will be:

Options

A. `61:29`
B. `61:28`
C. `60:29`
D. `59:29`

Answer

To solve the problem of finding the ratio of Sulphuric acid to water when three containers are mixed, we can follow these steps:

### Step 1: Determine the total parts of Sulphuric acid and water in each container.
- **Container 1:** The ratio of Sulphuric acid to water is 3:2.
- Total parts = 3 + 2 = 5
- Sulphuric acid = (3/5) of total volume
- Water = (2/5) of total volume

- **Container 2:** The ratio of Sulphuric acid to water is 7:3.
- Total parts = 7 + 3 = 10
- Sulphuric acid = (7/10) of total volume
- Water = (3/10) of total volume

- **Container 3:** The ratio of Sulphuric acid to water is 11:4.
- Total parts = 11 + 4 = 15
- Sulphuric acid = (11/15) of total volume
- Water = (4/15) of total volume

### Step 2: Assume a common capacity for each container.
Let’s assume the capacity of each container is 60 liters (this makes calculations easier).

### Step 3: Calculate the amount of Sulphuric acid and water in each container.
- **Container 1:**
- Sulphuric acid = (3/5) * 60 = 36 liters
- Water = (2/5) * 60 = 24 liters

- **Container 2:**
- Sulphuric acid = (7/10) * 60 = 42 liters
- Water = (3/10) * 60 = 18 liters

- **Container 3:**
- Sulphuric acid = (11/15) * 60 = 44 liters
- Water = (4/15) * 60 = 16 liters

### Step 4: Sum the amounts of Sulphuric acid and water from all containers.
- Total Sulphuric acid = 36 + 42 + 44 = 122 liters
- Total Water = 24 + 18 + 16 = 58 liters

### Step 5: Find the ratio of Sulphuric acid to water.
- Ratio of Sulphuric acid to water = 122:58

### Step 6: Simplify the ratio.
To simplify the ratio, we can divide both sides by their greatest common divisor (GCD). The GCD of 122 and 58 is 2.
- Simplified ratio = (122 ÷ 2):(58 ÷ 2) = 61:29

### Final Answer:
The ratio of Sulphuric acid to water in the mixture is **61:29**.

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