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

Options

A. 0.18
B. `18.5%`
C. `20.5%`
D. 0.2

Answer

To solve the problem step-by-step, we will follow these calculations:

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 480
- Discount Percentage = 10%
- Gain Percentage = 8%

### Step 2: Calculate the Selling Price (SP) after the discount
The discount amount can be calculated as follows:
\[ \text{Discount} = \text{Marked Price} \times \frac{\text{Discount Percentage}}{100} = 480 \times \frac{10}{100} = 48 \]
Now, we can find the Selling Price (SP):
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 480 - 48 = 432 \]

### Step 3: Calculate the Cost Price (CP) using the Gain Percentage
The gain is calculated as follows:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]
Given that the Gain Percentage is 8%, we can express it in terms of CP:
\[ \text{Gain Percentage} = \frac{\text{Gain}}{\text{Cost Price}} \times 100 \]
Let the Cost Price be \( CP \). Therefore:
\[ 8 = \frac{432 - CP}{CP} \times 100 \]
Rearranging gives:
\[ \frac{432 - CP}{CP} = \frac{8}{100} = 0.08 \]
Cross-multiplying yields:
\[ 432 - CP = 0.08 \times CP \]
Combining like terms:
\[ 432 = CP + 0.08 \times CP \]
\[ 432 = 1.08 \times CP \]
Now, solve for CP:
\[ CP = \frac{432}{1.08} = 400 \]

### Step 4: Calculate Gain Percentage if no discount is allowed
If no discount is allowed, the Selling Price (SP) would be equal to the Marked Price (MP), which is Rs. 480. Now we can calculate the gain:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = 480 - 400 = 80 \]
Now, we can find the Gain Percentage:
\[ \text{Gain Percentage} = \frac{\text{Gain}}{\text{Cost Price}} \times 100 = \frac{80}{400} \times 100 = 20\% \]

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

---