The marked price of an article is 60% more than its cost price. What maximum discount percentage can be offered by the shopkeeper to sell his article at no profit or no loss?

Options

A. 37.5
B. 62.5
C. 50
D. 25

Answer

To solve the problem step by step, we will first define the terms and then calculate the maximum discount percentage that can be offered by the shopkeeper to sell the article at no profit or no loss.

### Step 1: Define Cost Price (CP) and Marked Price (MP)
Let the Cost Price (CP) of the article be \( x \).

### Step 2: Calculate the Marked Price (MP)
According to the problem, the Marked Price (MP) is 60% more than the Cost Price (CP). Therefore, we can express the MP as:
\[ MP = CP + 60\% \text{ of } CP = x + 0.6x = 1.6x \]

### Step 3: Determine Selling Price for No Profit or Loss
To sell the article at no profit or no loss, the Selling Price (SP) must be equal to the Cost Price (CP). Thus:
\[ SP = CP = x \]

### Step 4: Calculate the Discount Offered
The discount is calculated based on the Marked Price (MP). The discount can be expressed as:
\[ \text{Discount} = MP - SP = 1.6x - x = 0.6x \]

### Step 5: Calculate the Discount Percentage
The discount percentage is given by the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{MP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Discount Percentage} = \left( \frac{0.6x}{1.6x} \right) \times 100 = \left( \frac{0.6}{1.6} \right) \times 100 \]

### Step 6: Simplify the Discount Percentage
Now, simplify \( \frac{0.6}{1.6} \):
\[ \frac{0.6}{1.6} = \frac{6}{16} = \frac{3}{8} \]
Now, substituting this back into the discount percentage formula:
\[ \text{Discount Percentage} = \left( \frac{3}{8} \right) \times 100 = 37.5\% \]

### Conclusion
The maximum discount percentage that can be offered by the shopkeeper to sell the article at no profit or no loss is **37.5%**.