`10%` of wheat sold by a Grocer is of lower quality. How much wheat of good quality should be mixed with 150 kg of wheat of lower quality quantity be `5%`?

Options

A. 150 kg
B. 135 kg
C. 50 kg
D. 85 kg

Answer

To solve the problem, we need to determine how much good quality wheat should be mixed with 150 kg of lower quality wheat so that the overall mixture has only 5% lower quality wheat.

### Step-by-Step Solution:

1. **Identify the Amount of Lower Quality Wheat**:
We have 150 kg of lower quality wheat.

2. **Calculate the Desired Percentage of Lower Quality Wheat**:
We want the final mixture to contain 5% lower quality wheat.

3. **Let the Amount of Good Quality Wheat be \( x \) kg**:
We will mix \( x \) kg of good quality wheat with the 150 kg of lower quality wheat.

4. **Calculate the Total Weight of the Mixture**:
The total weight of the mixture will be \( 150 + x \) kg.

5. **Set Up the Equation for Lower Quality Wheat**:
We know that the lower quality wheat should make up 5% of the total mixture:
\[ \frac{150}{150 + x} = 0.05 \]

6. **Cross Multiply to Solve for \( x \)**:
\[ 150 = 0.05(150 + x) \]
\[ 150 = 7.5 + 0.05x \]

7. **Rearranging the Equation**:
\[ 150 - 7.5 = 0.05x \]
\[ 142.5 = 0.05x \]

8. **Solve for \( x \)**:
\[ x = \frac{142.5}{0.05} \]
\[ x = 2850 \text{ kg} \]

### Conclusion:
To achieve a mixture that contains 5% lower quality wheat, the grocer should mix **2850 kg** of good quality wheat with the 150 kg of lower quality wheat.