A shopkeeper who marked his goals up by `30%` subsequently offered a discount of `10%` on the marked price. What is the percentage profit that the shopkeeper makes after offering the discount?

Options

A. `13%`
B. `17%`
C. `15%`
D. `23%`

Answer

To find the percentage profit that the shopkeeper makes after offering the discount, we can follow these steps:

### Step 1: Assume the Cost Price (CP)
Let's assume the cost price of the article is \( CP = 100 \) rupees.

### Step 2: Calculate the Marked Price (MP)
The shopkeeper marks up the price by \( 30\% \). Therefore, the marked price can be calculated as:
\[ MP = CP + (30\% \text{ of } CP) = 100 + (0.30 \times 100) = 100 + 30 = 130 \text{ rupees} \]

### Step 3: Calculate the Selling Price (SP)
The shopkeeper offers a discount of \( 10\% \) on the marked price. The discount amount is:
\[ \text{Discount} = 10\% \text{ of } MP = 0.10 \times 130 = 13 \text{ rupees} \]
Thus, the selling price after the discount is:
\[ SP = MP - \text{Discount} = 130 - 13 = 117 \text{ rupees} \]

### Step 4: Calculate the Profit
The profit can be calculated as:
\[ \text{Profit} = SP - CP = 117 - 100 = 17 \text{ rupees} \]

### Step 5: Calculate the Profit Percentage
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{17}{100} \right) \times 100 = 17\% \]

### Final Answer
The percentage profit that the shopkeeper makes after offering the discount is \( 17\% \).

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