After allowing a discount of ` 12(1)/(2)` % on the marked price of an article. it was sold for ₹700. Had the discount NOT been given, the profit would have been 60%.The cost price of the article is:

Options

A. ₹500
B. ₹540
C. ₹600
D. ₹480

Answer

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

### Step 1: Understand the Discount
The discount given is \( 12\frac{1}{2}\% \), which can be converted to a fraction:
\[ 12\frac{1}{2}\% = 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]

### Step 2: Determine Selling Price and Units
After the discount, the article was sold for ₹700. Since the discount is \( \frac{1}{8} \), the selling price corresponds to \( 7 \) units (as \( 8 - 1 = 7 \)):
\[ \text{Selling Price} = 7 \text{ units} = ₹700 \]

### Step 3: Calculate the Value of One Unit
To find the value of one unit:
\[ 1 \text{ unit} = \frac{700}{7} = ₹100 \]

### Step 4: Calculate the Marked Price
The marked price corresponds to \( 8 \) units:
\[ \text{Marked Price} = 8 \text{ units} = 8 \times 100 = ₹800 \]

### Step 5: Understand the Profit Scenario
If the discount had not been given, the selling price would have been equal to the marked price, which is ₹800. The problem states that this would have resulted in a profit of \( 60\% \).

### Step 6: Set Up the Equation for Cost Price
Let the cost price be \( CP \). A profit of \( 60\% \) means:
\[ \text{Selling Price} = CP + 60\% \text{ of } CP = CP + 0.6 \times CP = 1.6 \times CP \]
Setting this equal to the marked price:
\[ 1.6 \times CP = ₹800 \]

### Step 7: Solve for Cost Price
To find the cost price:
\[ CP = \frac{800}{1.6} = ₹500 \]

### Final Answer
The cost price of the article is ₹500.

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