A retailer purchase 40 pens at the cost price of 36 pens from a wholesaler. If he sells all of them at a discount of 3%, then what is his profit percent?

Options

A. 5
B. 9
C. 10
D. 12

Answer

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

### Step 1: Determine the Cost Price (CP) of each pen
The retailer purchases 40 pens at the cost price of 36 pens.

Let the cost price of one pen be Rs 1.

So, the total cost price for 36 pens = 36 * 1 = Rs 36.

### Step 2: Calculate the Cost Price for 40 pens
Since the retailer buys 40 pens for Rs 36, the cost price (CP) of each pen can be calculated as:

\[ \text{CP of each pen} = \frac{\text{Total CP}}{\text{Number of pens}} = \frac{36}{40} = Rs 0.90 \]

### Step 3: Determine the Selling Price (SP) after discount
The retailer sells each pen at a marked price of Rs 1. However, he gives a discount of 3%.

The selling price (SP) after the discount can be calculated as:

\[ \text{SP} = \text{Marked Price} - \text{Discount} = 1 - (3\% \text{ of } 1) = 1 - 0.03 = Rs 0.97 \]

### Step 4: Calculate the Profit
Now, we can calculate the profit made on each pen:

\[ \text{Profit} = \text{SP} - \text{CP} = 0.97 - 0.90 = Rs 0.07 \]

### Step 5: Calculate the Profit Percentage
The profit percentage can be calculated using the formula:

\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}} \times 100\right) = \left(\frac{0.07}{0.90} \times 100\right) \]

Calculating this gives:

\[ \text{Profit Percentage} = \left(\frac{0.07}{0.90}\right) \times 100 \approx 7.78\% \]

### Final Answer
The profit percentage is approximately **7.78%**.