What single discount is equivalent to two successive discounts of 20% and 15%?

Options

A. 0.35
B. 0.32
C. 0.34
D. 0.3

Answer

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

\[ \text{Equivalent Single Discount} = x + y - \left(\frac{x \cdot y}{100}\right) \]

where \(x\) and \(y\) are the two successive discounts.

### Step-by-Step Solution:

1. **Identify the Discounts**:
- Let \(x = 20\%\) (first discount)
- Let \(y = 15\%\) (second discount)

2. **Substitute the Values into the Formula**:
\[ \text{Equivalent Single Discount} = 20 + 15 - \left(\frac{20 \cdot 15}{100}\right) \]

3. **Calculate the Sum of Discounts**:
\[ 20 + 15 = 35 \]

4. **Calculate the Product of Discounts**:
\[ 20 \cdot 15 = 300 \]

5. **Divide the Product by 100**:
\[ \frac{300}{100} = 3 \]

6. **Subtract the Result from the Sum**:
\[ 35 - 3 = 32 \]

7. **Express as a Percentage**:
The equivalent single discount is \(32\%\).

### Final Answer:
The single discount equivalent to two successive discounts of 20% and 15% is **32%**.

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