A shopkeeper allows 25% discount on the marked price of an article and he suffered a loss of 15%. What will be the proit per cent if the article is sold at marked price ?

Options

A. 11.76
B. 12.12
C. 13.33
D. 14.28

Answer

To solve the problem step by step, we need to find out the profit percentage when the article is sold at the marked price (MP).

### Step 1: Understand the given information
- The shopkeeper allows a **25% discount** on the marked price (MP).
- He suffers a **15% loss** when selling at the discounted price.

### Step 2: Assume the Cost Price (CP)
Let's assume the Cost Price (CP) of the article is **100**.

### Step 3: Calculate the Selling Price (SP) after discount
Since there is a **15% loss**, the Selling Price (SP) can be calculated as:
\[ SP = CP - \text{Loss} \]
\[ SP = 100 - 15\% \text{ of } 100 \]
\[ SP = 100 - 15 = 85 \]

### Step 4: Relate Selling Price to Marked Price
Let the Marked Price (MP) be \( x \). Since a **25% discount** is given on the marked price, the Selling Price (SP) can also be expressed as:
\[ SP = MP - \text{Discount} \]
\[ SP = x - 25\% \text{ of } x \]
\[ SP = x - 0.25x = 0.75x \]

### Step 5: Set the two expressions for SP equal
From the previous steps, we have:
\[ 0.75x = 85 \]

### Step 6: Solve for Marked Price (MP)
To find \( x \):
\[ x = \frac{85}{0.75} \]
\[ x = 113.33 \]
So, the Marked Price (MP) is approximately **113.33**.

### Step 7: Calculate Profit Percentage when sold at Marked Price
Now, if the article is sold at the marked price, the Selling Price (SP) is \( 113.33 \). We can calculate the profit:
\[ \text{Profit} = SP - CP \]
\[ \text{Profit} = 113.33 - 100 = 13.33 \]

### Step 8: Calculate Profit Percentage
Profit percentage can be calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{13.33}{100} \right) \times 100 = 13.33\% \]

### Final Answer
The profit percentage when the article is sold at the marked price is **13.33%**.

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