The single discount equivalent to two successive discounts of 20% and 15% is:

Options

A. `28%`
B. `22%`
C. `30%`
D. `32%`

Answer

To find the single discount equivalent to two successive discounts of 20% and 15%, we can use the formula for calculating the equivalent discount when two discounts are applied successively. The formula is:

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

where \( A \) and \( B \) are the two successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \( A = 20\% \)
- Let \( B = 15\% \)

2. **Substitute the Values into the Formula**:
\[ \text{Equivalent Discount} = 20 + 15 - \frac{20 \times 15}{100} \]

3. **Calculate the Product of the Discounts**:
- Calculate \( 20 \times 15 = 300 \)

4. **Divide by 100**:
\[ \frac{300}{100} = 3 \]

5. **Combine the Values**:
\[ \text{Equivalent Discount} = 20 + 15 - 3 \]

6. **Perform the Final Calculation**:
\[ \text{Equivalent Discount} = 35 - 3 = 32 \]

Thus, the single discount equivalent to two successive discounts of 20% and 15% is **32%**.