A vessel full of 1600ltr milk. A person draws out 25% of milk from the vessel and replaced with water. He has repeated the same process 2 times more. Find the final amount of milk in the vessel?

Options

A. 675 L
B. 750 L
C. 800 L
D. 1200 L

Answer

To solve the problem, we will follow these steps:

### Step 1: Initial Amount of Milk
The initial amount of milk in the vessel is 1600 liters.

### Step 2: First Extraction
The person draws out 25% of the milk:
- 25% of 1600 liters = (25/100) * 1600 = 400 liters.
- After removing 400 liters, the amount of milk left = 1600 - 400 = 1200 liters.
- The amount of water added = 400 liters.

### Step 3: Second Extraction
Now, the vessel contains 1200 liters of milk and 400 liters of water (total 1600 liters). Again, 25% of the total liquid is drawn out:
- 25% of 1600 liters = 400 liters.
- The proportion of milk in the vessel is 1200/1600 = 3/4.
- Amount of milk removed = (3/4) * 400 = 300 liters.
- Amount of milk left after the second extraction = 1200 - 300 = 900 liters.

### Step 4: Third Extraction
Now, the vessel contains 900 liters of milk and 700 liters of water (total 1600 liters). Again, 25% of the total liquid is drawn out:
- 25% of 1600 liters = 400 liters.
- The proportion of milk in the vessel is 900/1600 = 9/16.
- Amount of milk removed = (9/16) * 400 = 225 liters.
- Amount of milk left after the third extraction = 900 - 225 = 675 liters.

### Final Result
The final amount of milk left in the vessel after three extractions is **675 liters**.

---