There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1, in the second container is 5:2. If they are mixed up, then the ratio of milk to water in the mixture will be?

Answer

To solve the problem step by step, we will calculate the amount of milk and water in each container, then combine them to find the final ratio of milk to water in the mixture.

### Step 1: Determine the quantities of milk and water in the first container.
- The ratio of milk to water in the first container is 3:1.
- Let the total quantity in the first container be 4 units (3 parts milk + 1 part water).
- Therefore, the quantity of milk in the first container = \( \frac{3}{4} \times \text{Total Capacity} \)
- The quantity of water in the first container = \( \frac{1}{4} \times \text{Total Capacity} \)

### Step 2: Determine the quantities of milk and water in the second container.
- The ratio of milk to water in the second container is 5:2.
- Let the total quantity in the second container be 7 units (5 parts milk + 2 parts water).
- Therefore, the quantity of milk in the second container = \( \frac{5}{7} \times \text{Total Capacity} \)
- The quantity of water in the second container = \( \frac{2}{7} \times \text{Total Capacity} \)

### Step 3: Equalize the total capacity of the containers.
- Since both containers have equal capacity, we can assume a common capacity for calculations. Let's assume the capacity of each container is 28 units (the least common multiple of 4 and 7).
- Thus, the total capacity of each container = 28 units.

### Step 4: Calculate the actual quantities of milk and water.
- For the first container:
- Milk = \( \frac{3}{4} \times 28 = 21 \) units
- Water = \( \frac{1}{4} \times 28 = 7 \) units

- For the second container:
- Milk = \( \frac{5}{7} \times 28 = 20 \) units
- Water = \( \frac{2}{7} \times 28 = 8 \) units

### Step 5: Combine the quantities from both containers.
- Total milk in the mixture = Milk from first container + Milk from second container
- Total milk = \( 21 + 20 = 41 \) units

- Total water in the mixture = Water from first container + Water from second container
- Total water = \( 7 + 8 = 15 \) units

### Step 6: Determine the final ratio of milk to water in the mixture.
- The final ratio of milk to water = Total milk : Total water
- Final ratio = \( 41 : 15 \)

### Final Answer:
The ratio of milk to water in the mixture is **41:15**.

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