A jar is filled with milk. A person replaces 25% of milk with water. He repeats the same process 5 times and as a result there is 1458ml of milk left in the jar. The remaining part of jar is filled with water. The initial quantity of milk in the jar was?

Options

A. 4.096 L
B. 6.144 L
C. 5.12 L
D. 9.216 L

Answer

To solve the problem, we need to determine the initial quantity of milk in the jar before the person started replacing it with water. The person replaces 25% of the milk with water 5 times, and after these operations, 1458 ml of milk remains.

### Step-by-Step Solution:

1. **Understanding the Replacement Process:**
Each time 25% of the milk is replaced with water, 75% of the milk remains. This means after one replacement, the quantity of milk left is 75% of the previous quantity.

2. **Mathematical Representation:**
If we denote the initial quantity of milk as \( V \), after one replacement, the quantity of milk left will be:
\[ \text{Milk after 1 replacement} = 0.75V \]

3. **Repeating the Process:**
After 5 replacements, the quantity of milk left can be represented as:
\[ \text{Milk after 5 replacements} = V \times (0.75)^5 \]

4. **Setting Up the Equation:**
We know that after 5 replacements, the quantity of milk left is 1458 ml. Therefore, we can set up the equation:
\[ V \times (0.75)^5 = 1458 \]

5. **Calculating \( (0.75)^5 \):**
First, calculate \( (0.75)^5 \):
\[ (0.75)^5 = 0.75 \times 0.75 \times 0.75 \times 0.75 \times 0.75 = 0.2373046875 \]

6. **Substituting Back into the Equation:**
Now substitute \( (0.75)^5 \) back into the equation:
\[ V \times 0.2373046875 = 1458 \]

7. **Solving for \( V \):**
To find \( V \), divide both sides by \( 0.2373046875 \):
\[ V = \frac{1458}{0.2373046875} \approx 6144 \]

8. **Conclusion:**
Therefore, the initial quantity of milk in the jar was approximately 6144 ml.

### Final Answer:
The initial quantity of milk in the jar was **6144 ml**.