A container contains 60 kg of milk. From this container 6 kg of milk was taken out and re placed by water. This process. was repeated further two times. The amount of milk left in the container is

Options

A. 34.24 kg
B. 39.64 kg
C. 43.74 kg
D. 47.6 kg

Answer

To solve the problem step by step, we will follow the process of calculating the amount of milk left in the container after repeatedly taking out some milk and replacing it with water.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial amount of milk in the container (I) = 60 kg
- Amount of milk taken out each time (V) = 6 kg
- Number of times the process is repeated (N) = 3

2. **Calculate the Fraction of Milk Remaining After Each Replacement**:
- After taking out 6 kg of milk from 60 kg, the fraction of milk remaining in the container is:
\[ \text{Fraction of milk remaining} = 1 - \frac{V}{I} = 1 - \frac{6}{60} = 1 - \frac{1}{10} = \frac{9}{10} \]

3. **Apply the Formula for Repeated Replacements**:
- The amount of milk left after N replacements can be calculated using the formula:
\[ \text{Final amount of milk} = I \times \left(1 - \frac{V}{I}\right)^N \]
- Substituting the values we have:
\[ \text{Final amount of milk} = 60 \times \left(\frac{9}{10}\right)^3 \]

4. **Calculate \(\left(\frac{9}{10}\right)^3\)**:
- \(\left(\frac{9}{10}\right)^3 = \frac{9 \times 9 \times 9}{10 \times 10 \times 10} = \frac{729}{1000}\)

5. **Calculate the Final Amount of Milk**:
- Now substitute back into the equation:
\[ \text{Final amount of milk} = 60 \times \frac{729}{1000} = \frac{60 \times 729}{1000} \]
- Calculate \(60 \times 729 = 43740\), so:
\[ \text{Final amount of milk} = \frac{43740}{1000} = 43.74 \text{ kg} \]

6. **Conclusion**:
- The amount of milk left in the container after the process is repeated three times is **43.74 kg**.