The single discount, which is equivalent to successive discounts of 25% and 10%, is :

Options

A. `35%`
B. `34.5%`
C. `33%`
D. `32.5%`

Answer

To find the single discount equivalent to successive discounts of 25% and 10%, we can use the formula for calculating the equivalent single discount:

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let the first discount (x) = 25%
- Let the second discount (y) = 10%

2. **Use the Formula**:
The formula for calculating the equivalent single discount (D) from two successive discounts is:
\[ D = x + y - \frac{xy}{100} \]

3. **Substitute the Values**:
Now, substitute the values of x and y into the formula:
\[ D = 25 + 10 - \frac{25 \times 10}{100} \]

4. **Calculate the Product**:
Calculate the product \( \frac{25 \times 10}{100} \):
\[ \frac{25 \times 10}{100} = \frac{250}{100} = 2.5 \]

5. **Complete the Calculation**:
Now, substitute this value back into the equation:
\[ D = 25 + 10 - 2.5 \]
\[ D = 35 - 2.5 = 32.5 \]

6. **Final Result**:
Therefore, the single discount equivalent to successive discounts of 25% and 10% is:
\[ \text{Single Discount} = 32.5\% \]