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

Options

A. Rs. 220
B. Rs. 200
C. Rs. 240
D. Rs. 260

Answer

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

### Step 1: Calculate the Selling Price (SP)
The merchant marks his goods at Rs. 300 and offers a discount of 25%.

To find the selling price after discount:
- Discount = 25% of Rs. 300
- Discount = (25/100) * 300 = Rs. 75

Now, subtract the discount from the marked price:
- Selling Price (SP) = Marked Price - Discount
- SP = 300 - 75 = Rs. 225

### Step 2: Use the Gain Percentage to Find the Cost Price (CP)
The merchant gains 12.5% on the cost price. We can use the formula for cost price based on selling price and gain percentage:
- CP = SP * (100 / (100 + Gain Percentage))

Substituting the values:
- Gain Percentage = 12.5%
- CP = 225 * (100 / (100 + 12.5))
- CP = 225 * (100 / 112.5)

### Step 3: Simplify the Calculation
Now, calculate the fraction:
- CP = 225 * (100 / 112.5) = 225 * (8 / 9) [since 100/112.5 = 8/9]

### Step 4: Calculate the Final Cost Price
Now, multiply:
- CP = 225 * (8 / 9) = 200

Thus, the cost price of the article is Rs. 200.

### Summary of the Solution:
- Selling Price (SP) = Rs. 225
- Cost Price (CP) = Rs. 200

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