Even after reducing the marked price of a pen by Rs 32, a shopkeeper makes a profit of 15%. If the cost price be Rs 320, what percentage of profit does he make it he sells the pen at the marked price?

Answer

To solve the problem step by step, we will follow the given information and calculations.

### Step 1: Identify the given values
- Cost Price (CP) of the pen = Rs 320
- Profit Percentage after reducing the marked price = 15%

### Step 2: Calculate the Selling Price (SP) after the reduction
The selling price can be calculated using the formula:
\[ SP = CP + \text{Profit} \]
Where Profit is calculated as:
\[ \text{Profit} = \frac{\text{Profit Percentage}}{100} \times CP \]
Substituting the values:
\[ \text{Profit} = \frac{15}{100} \times 320 = 48 \]
Now, calculate the Selling Price:
\[ SP = 320 + 48 = 368 \]

### Step 3: Calculate the Marked Price (MP)
According to the problem, the marked price is Rs 32 more than the selling price after the reduction. Therefore:
\[ MP = SP + 32 = 368 + 32 = 400 \]

### Step 4: Calculate the profit when selling at the marked price
Now, if the pen is sold at the marked price (MP), the new Selling Price (SP) is Rs 400. We need to calculate the profit:
\[ \text{Profit} = MP - CP = 400 - 320 = 80 \]

### Step 5: Calculate the profit percentage when selling at the marked price
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{80}{320}\right) \times 100 = 25\% \]

### Conclusion
The profit percentage when the pen is sold at the marked price is **25%**.

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