2 equal containers have milk and water in the ratio 2: 1 and 3 :1 . Respectively , If both containers are emptied into a bigger container, then find the ratio of milk to water in bigger container ?

Answer

To solve the problem of finding the ratio of milk to water in the bigger container after combining the contents of two equal containers, we can follow these steps:

### Step 1: Understand the Ratios
We have two containers:
- Container A has milk and water in the ratio of 2:1.
- Container B has milk and water in the ratio of 3:1.

### Step 2: Assume Equal Capacity
Let’s assume each container has a capacity of 1 liter for simplicity. This means:
- For Container A:
- Total parts = 2 (milk) + 1 (water) = 3 parts.
- Milk in A = (2/3) * 1 liter = 2/3 liters.
- Water in A = (1/3) * 1 liter = 1/3 liters.

- For Container B:
- Total parts = 3 (milk) + 1 (water) = 4 parts.
- Milk in B = (3/4) * 1 liter = 3/4 liters.
- Water in B = (1/4) * 1 liter = 1/4 liters.

### Step 3: Combine the Quantities
Now, we will combine the milk and water from both containers into a bigger container:
- Total milk = Milk from A + Milk from B = (2/3) + (3/4).
- Total water = Water from A + Water from B = (1/3) + (1/4).

### Step 4: Find a Common Denominator
To add the fractions, we need a common denominator:
- The least common multiple of 3 and 4 is 12.

Calculating the total milk:
- Milk from A = (2/3) = (2 * 4)/(3 * 4) = 8/12 liters.
- Milk from B = (3/4) = (3 * 3)/(4 * 3) = 9/12 liters.
- Total milk = 8/12 + 9/12 = 17/12 liters.

Calculating the total water:
- Water from A = (1/3) = (1 * 4)/(3 * 4) = 4/12 liters.
- Water from B = (1/4) = (1 * 3)/(4 * 3) = 3/12 liters.
- Total water = 4/12 + 3/12 = 7/12 liters.

### Step 5: Determine the Ratio
Now we can find the ratio of milk to water in the bigger container:
- Ratio of milk to water = Total milk : Total water = (17/12) : (7/12).

Since the denominators are the same, we can simplify this to:
- Ratio of milk to water = 17 : 7.

### Final Answer
The ratio of milk to water in the bigger container is **17 : 7**.

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