What is the single discount equivalent to two successive discounts of 10% and 15%?

Options

A. `21.5%`
B. `23.5%`
C. `25%`
D. `26.5%`

Answer

To find the single discount equivalent to two successive discounts of 10% and 15%, we can use the formula for calculating the net discount when two discounts are applied successively. The formula is:

\[ \text{Net Discount} = A + B - \frac{A \times B}{100} \]

Where:
- \( A \) is the first discount percentage (10% in this case)
- \( B \) is the second discount percentage (15% in this case)

### Step-by-Step Solution:

1. **Identify the Discounts:**
- Let \( A = 10\% \)
- Let \( B = 15\% \)

2. **Apply the Formula:**
- Substitute the values of \( A \) and \( B \) into the formula:
\[ \text{Net Discount} = 10 + 15 - \frac{10 \times 15}{100} \]

3. **Calculate the Product of Discounts:**
- Calculate \( \frac{10 \times 15}{100} \):
\[ \frac{150}{100} = 1.5 \]

4. **Substitute Back into the Formula:**
- Now substitute back into the formula:
\[ \text{Net Discount} = 10 + 15 - 1.5 \]

5. **Perform the Addition and Subtraction:**
- Calculate \( 10 + 15 = 25 \)
- Then subtract \( 1.5 \):
\[ 25 - 1.5 = 23.5 \]

6. **Conclusion:**
- The single discount equivalent to two successive discounts of 10% and 15% is:
\[ \text{Net Discount} = 23.5\% \]

### Final Answer:
The single discount equivalent to two successive discounts of 10% and 15% is **23.5%**.