The marked price of a radio is Rs. 480. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be

Options

A. `18%`
B. `18.5%`
C. `20.5%`
D. `20%`

Answer

To solve the problem step by step, we will follow the information provided and calculate the required values.

### Step 1: Identify the Given Information
- Marked Price (MP) = Rs. 480
- Discount = 10%
- Gain (Profit) with discount = 8%

### Step 2: Calculate the Selling Price (SP) after Discount
Since the shopkeeper allows a discount of 10%, we can calculate the selling price (SP) as follows:
\[ \text{SP} = \text{MP} - \text{Discount} \]
\[ \text{Discount} = 10\% \text{ of } 480 = \frac{10}{100} \times 480 = 48 \]
\[ \text{SP} = 480 - 48 = 432 \]

### Step 3: Calculate the Cost Price (CP)
We know that the gain is 8%. The selling price is related to the cost price by the formula:
\[ \text{SP} = \text{CP} + \text{Gain} \]
Given that Gain = 8% of CP, we can express this as:
\[ \text{SP} = \text{CP} + 0.08 \times \text{CP} = 1.08 \times \text{CP} \]
Now substituting the value of SP:
\[ 432 = 1.08 \times \text{CP} \]
To find CP, we rearrange the equation:
\[ \text{CP} = \frac{432}{1.08} \]
Calculating this gives:
\[ \text{CP} = 400 \]

### Step 4: Calculate Gain Percent if No Discount is Allowed
If no discount is allowed, the selling price would be equal to the marked price, which is Rs. 480. Now we can calculate the profit:
\[ \text{Profit} = \text{SP (no discount)} - \text{CP} \]
\[ \text{Profit} = 480 - 400 = 80 \]
Now, we can calculate the gain percent:
\[ \text{Gain Percent} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
\[ \text{Gain Percent} = \left(\frac{80}{400}\right) \times 100 = 20\% \]

### Final Answer
If no discount is allowed, the gain percent would be **20%**.

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