20% discount is offered on an item. By applying a promo code Rishi wins 4% cash back. What is the equivalent single discount?

Options

A. 0.33
B. 0.232
C. 0.226
D. 0.24

Answer

To find the equivalent single discount when a 20% discount is offered along with a 4% cashback, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Discounts**:
- The first discount is 20%.
- The second discount (cashback) is 4%.

2. **Use the Formula for Equivalent Single Discount**:
The formula to calculate the equivalent single discount (ESD) when two discounts are applied is:
\[ ESD = D_1 + D_2 - \left(\frac{D_1 \times D_2}{100}\right) \]
where \(D_1\) is the first discount and \(D_2\) is the second discount.

3. **Substitute the Values**:
- Here, \(D_1 = 20\%\) and \(D_2 = 4\%\).
\[ ESD = 20 + 4 - \left(\frac{20 \times 4}{100}\right) \]

4. **Calculate the Product of Discounts**:
\[ D_1 \times D_2 = 20 \times 4 = 80 \]
Now, divide this by 100:
\[ \frac{80}{100} = 0.8 \]

5. **Calculate the Equivalent Single Discount**:
Now substitute back into the formula:
\[ ESD = 20 + 4 - 0.8 \]
\[ ESD = 24 - 0.8 = 23.2 \]

6. **Convert to Percentage**:
The equivalent single discount is 23.2%.

### Final Answer:
The equivalent single discount is **23.2%**.