A merchant marks his goods at ₹ 900 and allows a discount of `25%`'. If he still gain `12.5%`, then the cost price of the article is :

Options

A. ₹ 500
B. ₹ 600
C. ₹ 720
D. can't be determined

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Identify the given values
- Marked Price (MP) = ₹900
- Discount = 25%
- Profit = 12.5%

### Step 2: Calculate the Selling Price (SP)
The Selling Price can be calculated using the formula:
\[ SP = MP - (Discount \% \times MP) \]
Substituting the values:
\[ SP = 900 - (25\% \times 900) \]
\[ SP = 900 - (0.25 \times 900) \]
\[ SP = 900 - 225 \]
\[ SP = ₹675 \]

### Step 3: Relate Selling Price to Cost Price
We know that:
\[ SP = CP + Profit \]
Where Profit can be expressed as:
\[ Profit = \frac{Profit \%}{100} \times CP \]
Thus:
\[ SP = CP + \left(\frac{12.5}{100} \times CP\right) \]
This can be rewritten as:
\[ SP = CP \left(1 + \frac{12.5}{100}\right) \]
\[ SP = CP \left(1 + 0.125\right) \]
\[ SP = CP \times 1.125 \]

### Step 4: Solve for Cost Price (CP)
Now we can substitute the Selling Price we calculated:
\[ 675 = CP \times 1.125 \]
To find CP, divide both sides by 1.125:
\[ CP = \frac{675}{1.125} \]
Calculating this gives:
\[ CP = 600 \]

### Conclusion
The Cost Price of the article is **₹600**.