Find the single discount equivalent to two successive discounts of 20% and 10%.

Options

A. A) 28%
B. B) 25%
C. C) 26%
D. D) 30%

Answer

To find the single discount equivalent to two successive discounts of 20% and 10%, we can use the formula for calculating the equivalent single discount. The formula is:

\[ \text{Single Discount} = A + B - \left(\frac{A \times B}{100}\right) \]

where \( A \) is the first discount percentage and \( B \) is the second discount percentage.

### Step-by-Step Solution:

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

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

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

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

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

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

7. **Final Result:**
The single discount equivalent to the two successive discounts of 20% and 10% is **28%**.