A merchant marks the price of his articles 30% above the cost price. He gives some discount on it and earns a profit of 13.75%. What is the discount percentage?

Options

A. 12.5
B. 13.75
C. 16.25
D. 10.25

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) of the article be \(100\).

### Step 2: Calculate the Marked Price (MP)
The merchant marks the price 30% above the cost price. Therefore, the Marked Price (MP) can be calculated as follows:
\[ MP = CP + 30\% \text{ of } CP = 100 + 30\% \text{ of } 100 = 100 + 30 = 130 \]

### Step 3: Calculate the Selling Price (SP)
The merchant earns a profit of 13.75%. The Selling Price (SP) can be calculated using the formula:
\[ SP = CP + \text{Profit} = CP + \left(\frac{\text{Profit \%}}{100} \times CP\right) \]
Substituting the values:
\[ SP = 100 + \left(\frac{13.75}{100} \times 100\right) = 100 + 13.75 = 113.75 \]

### Step 4: Relate Selling Price, Marked Price, and Discount
The Selling Price (SP) is also related to the Marked Price (MP) and the Discount (D) as follows:
\[ SP = MP - D \]
Substituting the values we have:
\[ 113.75 = 130 - D \]

### Step 5: Solve for Discount (D)
Rearranging the equation to find D:
\[ D = 130 - 113.75 = 16.25 \]

### Step 6: Calculate the Discount Percentage
The discount percentage can be calculated using the formula:
\[ \text{Discount Percentage} = \left(\frac{D}{MP}\right) \times 100 \]
Substituting the values:
\[ \text{Discount Percentage} = \left(\frac{16.25}{130}\right) \times 100 \approx 12.5\% \]

### Final Answer
The discount percentage is **12.5%**.

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