A retailer purchased radiosets at the rate of Rs 400 each from a wholesaler. He raised the price by 30% and then allowed a discount of 8% on each set. His profit percent will be

Options

A. 19%
B. 7.84%
C. 22%
D. 19.6%

Answer

To find the profit percentage of the retailer who purchased radiosets at Rs 400 each, raised the price by 30%, and then allowed an 8% discount, we can follow these steps:

### Step 1: Calculate the Marked Price (MP)
The retailer raised the price by 30%. The formula to calculate the marked price is:

\[ \text{MP} = \text{CP} + \left(\frac{30}{100} \times \text{CP}\right) \]

Where CP (Cost Price) = Rs 400.

Calculating the MP:

\[ \text{MP} = 400 + \left(\frac{30}{100} \times 400\right) = 400 + 120 = 520 \]

### Step 2: Calculate the Selling Price (SP)
The retailer allowed an 8% discount on the marked price. The formula for selling price after discount is:

\[ \text{SP} = \text{MP} - \left(\frac{8}{100} \times \text{MP}\right) \]

Calculating the SP:

\[ \text{SP} = 520 - \left(\frac{8}{100} \times 520\right) = 520 - 41.6 = 478.4 \]

### Step 3: Calculate the Profit
Profit can be calculated using the formula:

\[ \text{Profit} = \text{SP} - \text{CP} \]

Calculating the profit:

\[ \text{Profit} = 478.4 - 400 = 78.4 \]

### Step 4: Calculate the Profit Percentage
Profit percentage is calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]

Calculating the profit percentage:

\[ \text{Profit Percentage} = \left(\frac{78.4}{400}\right) \times 100 = 19.6\% \]

### Conclusion
The profit percentage of the retailer is **19.6%**.

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