A container contained 80 kg of milk. From this container, 8 kg of milk was taken out and replaced by water. This process was further repeated two times. How much milk is now contained by the container?

Options

A. 48 kg
B. 56 kg
C. 58.32 kg
D. 59.64 kg

Answer

To solve the problem step by step, we will use the formula for finding the remaining quantity of milk after repeatedly replacing a portion with water.

### Step-by-Step Solution:

1. **Identify Initial Values**:
- Initial quantity of milk (A) = 80 kg
- Quantity of milk taken out (X) = 8 kg
- Total quantity of the container (C) = 80 kg
- Number of times the process is repeated (N) = 3

2. **Calculate the Fraction of Milk Remaining After Each Replacement**:
- The fraction of milk remaining after each replacement can be calculated as:
\[ \text{Fraction of milk remaining} = 1 - \frac{X}{C} = 1 - \frac{8}{80} = 1 - 0.1 = 0.9 \]

3. **Apply the Formula for N Replacements**:
- The formula to find the remaining quantity of milk after N replacements is:
\[ \text{Remaining Milk} = A \times \left( \frac{C - X}{C} \right)^N \]
- Substituting the values we have:
\[ \text{Remaining Milk} = 80 \times \left( \frac{80 - 8}{80} \right)^3 = 80 \times (0.9)^3 \]

4. **Calculate \( (0.9)^3 \)**:
- Calculate \( (0.9)^3 \):
\[ (0.9)^3 = 0.729 \]

5. **Calculate the Remaining Milk**:
- Now, substitute back to find the remaining milk:
\[ \text{Remaining Milk} = 80 \times 0.729 = 58.32 \text{ kg} \]

### Final Answer:
The amount of milk now contained in the container is **58.32 kg**.

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