10% discount is offered on an item By applying a promo code the customer wins 20% cash back. What is the effective discount?

Options

A. 0.336
B. 0.3
C. 0.22
D. 0.28

Answer

To find the effective discount when a 10% discount is offered on an item and a 20% cash back is received, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Original Price**:
Let's assume the original price of the item is \( P = 100 \) units.

**Hint**: Always start by assuming a base price to simplify calculations.

2. **Calculate the Discount Amount**:
The discount offered is 10% of the original price.
\[ \text{Discount} = 10\% \text{ of } 100 = \frac{10}{100} \times 100 = 10 \text{ units} \]

**Hint**: To find the discount amount, multiply the percentage by the original price.

3. **Calculate the Price After Discount**:
Subtract the discount from the original price.
\[ \text{Price after discount} = 100 - 10 = 90 \text{ units} \]

**Hint**: The new price is simply the original price minus the discount.

4. **Calculate the Cash Back Amount**:
The customer receives 20% cash back on the discounted price.
\[ \text{Cash back} = 20\% \text{ of } 90 = \frac{20}{100} \times 90 = 18 \text{ units} \]

**Hint**: Cash back is calculated based on the price after the discount.

5. **Calculate the Effective Price After Cash Back**:
Subtract the cash back from the price after the discount.
\[ \text{Effective price} = 90 - 18 = 72 \text{ units} \]

**Hint**: The effective price is the discounted price minus any cash back received.

6. **Calculate the Effective Discount**:
Now, we find the effective discount by comparing the original price and the effective price.
\[ \text{Effective discount} = \frac{100 - 72}{100} \times 100 = \frac{28}{100} \times 100 = 28\% \]

**Hint**: The effective discount is calculated as the difference between the original price and the effective price, divided by the original price, then multiplied by 100 to get a percentage.

### Conclusion:
The effective discount on the item is **28%**.