What is the net discount (in %) for successive discounts of 10% and 20%?

Options

A. 23
B. 70
C. 75
D. 28

Answer

To find the net discount for successive discounts of 10% and 20%, we can use the formula for calculating the net discount when two successive discounts are applied. The formula is:

\[ \text{Net Discount} = d_1 + d_2 - \left(\frac{d_1 \times d_2}{100}\right) \]

Where:
- \(d_1\) is the first discount percentage (10% in this case)
- \(d_2\) is the second discount percentage (20% in this case)

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \(d_1 = 10\%\)
- Let \(d_2 = 20\%\)

2. **Substitute the Values into the Formula**:
\[ \text{Net Discount} = 10 + 20 - \left(\frac{10 \times 20}{100}\right) \]

3. **Calculate the Product of the Discounts**:
\[ 10 \times 20 = 200 \]

4. **Divide by 100**:
\[ \frac{200}{100} = 2 \]

5. **Substitute Back into the Formula**:
\[ \text{Net Discount} = 10 + 20 - 2 \]

6. **Perform the Addition and Subtraction**:
\[ \text{Net Discount} = 30 - 2 = 28 \]

7. **Final Result**:
- The net discount is \(28\%\).

### Conclusion:
The net discount for successive discounts of 10% and 20% is **28%**.