A shopkeeper used to allow a discount of Rs. 20 on a product. He double the discount on the product and sold it for Rs. 80. What was the percentage of discount offered ?

Options

A. `20%`
B. `25%`
C. `30%`
D. `33.33%`

Answer

To solve the problem step by step, we need to determine the original marked price of the product and then calculate the percentage of the discount offered.

### Step 1: Understand the initial discount
The shopkeeper initially allows a discount of Rs. 20 on the product.

### Step 2: Calculate the new discount
Since the shopkeeper doubles the discount, the new discount becomes:
\[ \text{New Discount} = 2 \times 20 = Rs. 40 \]

### Step 3: Determine the selling price
The selling price after applying the new discount is given as Rs. 80.

### Step 4: Calculate the marked price
Let the marked price (MP) be \( x \). The selling price (SP) is calculated as:
\[ \text{SP} = \text{MP} - \text{New Discount} \]
Substituting the known values:
\[ 80 = x - 40 \]
Now, solve for \( x \):
\[ x = 80 + 40 \]
\[ x = 120 \]
So, the marked price is Rs. 120.

### Step 5: Calculate the discount amount
The discount amount offered by the shopkeeper after doubling is Rs. 40.

### Step 6: Calculate the percentage of discount
The percentage of discount can be calculated using the formula:
\[ \text{Percentage Discount} = \left( \frac{\text{Discount Amount}}{\text{Marked Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Discount} = \left( \frac{40}{120} \right) \times 100 \]
\[ \text{Percentage Discount} = \frac{1}{3} \times 100 \]
\[ \text{Percentage Discount} = 33.33\% \]

### Final Answer
The percentage of discount offered is **33.33%**.

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