A vessel contains 400 ltof milk. 20 ltof milk taken out from it and replaced by water. Then again from mixture 20 ltare taken out and replaced by water. Find the ratio of milk and water in the result ant mixture

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Initial Setup
We have a vessel containing 400 liters of milk.

### Step 2: First Replacement
We take out 20 liters of milk from the vessel.
- Amount of milk left = 400 liters - 20 liters = 380 liters.
- We then replace the 20 liters taken out with water.
- Now the total volume in the vessel remains 400 liters, but the composition changes to 380 liters of milk and 20 liters of water.

### Step 3: Second Replacement
Next, we take out 20 liters from the mixture (which now contains both milk and water).
- The ratio of milk to the total mixture after the first replacement is:
- Milk = 380 liters
- Water = 20 liters
- Total = 400 liters
- The fraction of milk in the mixture = 380/400 = 0.95
- The amount of milk in the 20 liters taken out = 20 liters * 0.95 = 19 liters.
- The amount of water in the 20 liters taken out = 20 liters - 19 liters = 1 liter.

After taking out 20 liters of the mixture:
- Milk left = 380 liters - 19 liters = 361 liters.
- Water left = 20 liters - 1 liter = 19 liters.

Now we replace the 20 liters taken out with water:
- Total volume remains 400 liters.
- New amount of water = 19 liters + 20 liters = 39 liters.

### Step 4: Final Calculation
Now we have:
- Milk = 361 liters
- Water = 39 liters

### Step 5: Ratio of Milk to Water
To find the ratio of milk to water:
- Ratio = Milk : Water = 361 : 39

### Final Answer
The ratio of milk to water in the resultant mixture is **361:39**.

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