Alex sold his goods after annoucing two successive discounts of 30% each. The effective discount altogether is

Options

A. `52%`
B. `49%`
C. `50%`
D. `51%`

Answer

To find the effective discount when two successive discounts of 30% each are applied, we can use the formula for successive discounts:

\[ \text{Effective Discount} = d_1 + d_2 - \left(\frac{d_1 \times d_2}{100}\right) \]

Where:
- \(d_1\) is the first discount percentage
- \(d_2\) is the second discount percentage

### Step-by-step Solution:

1. **Identify the Discounts:**
- Let \(d_1 = 30\%\)
- Let \(d_2 = 30\%\)

2. **Substitute the Values into the Formula:**
\[ \text{Effective Discount} = 30 + 30 - \left(\frac{30 \times 30}{100}\right) \]

3. **Calculate the Product of the Discounts:**
\[ 30 \times 30 = 900 \]

4. **Divide by 100:**
\[ \frac{900}{100} = 9 \]

5. **Substitute Back into the Formula:**
\[ \text{Effective Discount} = 30 + 30 - 9 \]

6. **Perform the Addition and Subtraction:**
\[ \text{Effective Discount} = 60 - 9 = 51 \]

### Final Answer:
The effective discount altogether is **51%**.

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