A Jar was full of milk. A person used to draw out 18. 75% of the milk from the jar and replaced it with salt solution. He has repeated the same process 3 times and thus there was only 4L 394ml of milk left in the jar, the rest part of a jar was filled with salt solution. The initial amount of milk in the Jar was?

Options

A. 4.096L
B. 8.192L
C. 6.144L
D. 8.782L

Answer

To find the initial amount of milk in the jar, we will follow these steps:

### Step 1: Understand the Problem
We know that 18.75% of the milk is drawn out and replaced with salt solution. This process is repeated 3 times, and after these operations, there is 4 liters and 394 milliliters of milk left in the jar.

### Step 2: Convert the Remaining Milk to Milliliters
Since we are dealing with milliliters and liters, let's convert the remaining milk into milliliters:
- 4 liters = 4000 milliliters
- Therefore, 4 liters and 394 milliliters = 4000 ml + 394 ml = **4394 milliliters**.

### Step 3: Define Variables
Let the initial amount of milk in the jar be \( x \) milliliters.

### Step 4: Calculate the Amount of Milk Remaining After Each Extraction
When 18.75% of the milk is drawn out, 81.25% remains. We can express this as:
- Remaining milk after one extraction = \( x \times \left(1 - \frac{18.75}{100}\right) = x \times 0.8125 \).

After repeating this process 3 times, the amount of milk left can be expressed as:
- Remaining milk after 3 extractions = \( x \times (0.8125)^3 \).

### Step 5: Set Up the Equation
We know that after 3 extractions, the remaining milk is 4394 ml. Therefore, we can set up the equation:
\[ x \times (0.8125)^3 = 4394 \]

### Step 6: Calculate \( (0.8125)^3 \)
Calculating \( (0.8125)^3 \):
\[ (0.8125)^3 = 0.8125 \times 0.8125 \times 0.8125 = 0.512 \]
(You can use a calculator for precise calculation.)

### Step 7: Substitute and Solve for \( x \)
Now substitute \( (0.8125)^3 \) back into the equation:
\[ x \times 0.512 = 4394 \]
To find \( x \):
\[ x = \frac{4394}{0.512} \]

### Step 8: Calculate \( x \)
Calculating \( x \):
\[ x \approx 8585.94 \text{ milliliters} \]

### Step 9: Convert Milliliters to Liters
To convert milliliters back to liters:
\[ x \approx \frac{8585.94}{1000} \approx 8.586 \text{ liters} \]

### Conclusion
The initial amount of milk in the jar was approximately **8.586 liters**.