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

Options

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

Answer

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

### Step 1: Calculate the Discount Amount
The marked price of the goods is Rs. 900, and the discount allowed is 25%.

\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) \]

\[ \text{Discount} = 900 \times \left(\frac{25}{100}\right) = 900 \times 0.25 = 225 \]

### Step 2: Calculate the Selling Price
Now, we subtract the discount from the marked price to find the selling price.

\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]

\[ \text{Selling Price} = 900 - 225 = 675 \]

### Step 3: Use the Selling Price to Find the Cost Price
Given that the merchant gains a profit of 12.5%, we can use the formula for cost price based on selling price and profit percentage.

\[ \text{Cost Price} = \frac{100}{100 + \text{Gain Percentage}} \times \text{Selling Price} \]

Substituting the values:

\[ \text{Cost Price} = \frac{100}{100 + 12.5} \times 675 \]

\[ \text{Cost Price} = \frac{100}{112.5} \times 675 \]

### Step 4: Simplify the Calculation
Now we can simplify the fraction and multiply:

\[ \text{Cost Price} = \frac{100 \times 675}{112.5} \]

Calculating \( \frac{675}{112.5} \):

\[ 675 \div 112.5 = 6 \]

Now, multiply by 100:

\[ \text{Cost Price} = 100 \times 6 = 600 \]

### Final Answer
The cost price of the article is Rs. 600.

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