A merchant marks his goods at ₹ 300 and allows a discount of `25%`. If he still gains 12.5%, then the cost price of article is:

Options

A. ₹ 220
B. ₹ 200
C. ₹ 240
D. ₹ 260

Answer

To find the cost price of the article, we can follow these steps:

### Step 1: Understand the given information
- Marked Price (MP) = ₹300
- Discount = 25%
- Profit = 12.5%

### Step 2: Calculate the Selling Price (SP)
The Selling Price (SP) can be calculated after applying the discount on the Marked Price.

\[ \text{Discount Amount} = \text{Marked Price} \times \left(\frac{\text{Discount}}{100}\right) \]
\[ \text{Discount Amount} = 300 \times \left(\frac{25}{100}\right) = 300 \times 0.25 = ₹75 \]

Now, calculate the Selling Price:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount Amount} \]
\[ \text{Selling Price} = 300 - 75 = ₹225 \]

### Step 3: Relate Selling Price to Cost Price
We know that the Selling Price is related to the Cost Price (CP) and the Profit Percentage. The formula for Selling Price in terms of Cost Price and Profit Percentage is:

\[ \text{Selling Price} = \text{Cost Price} + \left(\text{Cost Price} \times \frac{\text{Profit}}{100}\right) \]

This can also be expressed as:
\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit}}{100}\right) \]
Substituting the known values:
\[ 225 = \text{Cost Price} \times \left(1 + \frac{12.5}{100}\right) \]
\[ 225 = \text{Cost Price} \times 1.125 \]

### Step 4: Solve for Cost Price
Now, we can solve for the Cost Price:
\[ \text{Cost Price} = \frac{225}{1.125} \]
Calculating the division:
\[ \text{Cost Price} = 200 \]

### Final Answer
The cost price of the article is ₹200.

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