What is the net discount for two successive discounts of 10% and 40%?

Options

A. `44%`
B. `46%`
C. `54%`
D. `56%`

Answer

To find the net discount for two successive discounts of 10% and 40%, we can use the formula:

\[ \text{Net Discount} = x + y - \frac{xy}{100} \]

where:
- \( x \) is the first discount (10%),
- \( y \) is the second discount (40%).

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \( x = 10 \) (first discount)
- Let \( y = 40 \) (second discount)

2. **Substitute the Values into the Formula**:
\[ \text{Net Discount} = 10 + 40 - \frac{10 \times 40}{100} \]

3. **Calculate \( xy \)**:
\[ xy = 10 \times 40 = 400 \]

4. **Calculate \( \frac{xy}{100} \)**:
\[ \frac{xy}{100} = \frac{400}{100} = 4 \]

5. **Substitute Back into the Formula**:
\[ \text{Net Discount} = 10 + 40 - 4 \]

6. **Perform the Addition and Subtraction**:
\[ \text{Net Discount} = 50 - 4 = 46 \]

### Final Answer:
The net discount for two successive discounts of 10% and 40% is **46%**.