An ore contains `5%` copper. How much ore is required to obtain `400 g` of copper?

Options

A. `2kg`
B. `4kg`
C. `6kg`
D. `8kg`

Answer

To solve the problem of how much ore is required to obtain 400 grams of copper when the ore contains 5% copper, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem:**
- We know that the ore contains 5% copper. This means that for every 100 grams of ore, there are 5 grams of copper.

2. **Set Up the Equation:**
- Let the amount of ore required be \( x \) grams.
- Since 5% of the ore is copper, we can express this as:
\[ 5\% \text{ of } x = 400 \text{ grams of copper} \]
- This can be written mathematically as:
\[ \frac{5}{100} \times x = 400 \]

3. **Simplify the Equation:**
- To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ 5x = 400 \times 100 \]
- This simplifies to:
\[ 5x = 40000 \]

4. **Solve for \( x \):**
- Now, divide both sides by 5 to find \( x \):
\[ x = \frac{40000}{5} \]
- Calculating this gives:
\[ x = 8000 \text{ grams} \]

5. **Convert Grams to Kilograms:**
- Since the answer is often required in kilograms, we convert grams to kilograms:
\[ 8000 \text{ grams} = \frac{8000}{1000} \text{ kg} = 8 \text{ kg} \]

### Final Answer:
The amount of ore required to obtain 400 grams of copper is **8 kg**.