A person sells an article at 10% below its cost price. Had he sold it for Rs. 332 more, he would have made a profit of 20%. What is the original selling price (in Rs.) of the article?

Options

A. 996
B. 1028
C. 1328
D. 896

Answer

To solve the problem step by step, we will denote the cost price (CP) of the article as \( CP \).

### Step 1: Define the Selling Price (SP)
The person sells the article at 10% below its cost price. Therefore, the selling price (SP) can be expressed as:
\[ SP = CP - 0.1 \times CP = 0.9 \times CP \]

### Step 2: Determine the Selling Price for Profit
If the person sells the article for Rs. 332 more, he would make a profit of 20%. The selling price at a 20% profit can be expressed as:
\[ SP_{profit} = CP + 0.2 \times CP = 1.2 \times CP \]

### Step 3: Set Up the Equation
According to the problem, the difference between the selling price at a 20% profit and the original selling price is Rs. 332. Therefore, we can set up the equation:
\[ SP_{profit} - SP = 332 \]
Substituting the expressions for \( SP_{profit} \) and \( SP \):
\[ 1.2 \times CP - 0.9 \times CP = 332 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ (1.2 - 0.9) \times CP = 332 \]
\[ 0.3 \times CP = 332 \]

### Step 5: Solve for Cost Price (CP)
To find the cost price, divide both sides by 0.3:
\[ CP = \frac{332}{0.3} = 1106.67 \]

### Step 6: Calculate the Original Selling Price (SP)
Now that we have the cost price, we can find the original selling price:
\[ SP = 0.9 \times CP = 0.9 \times 1106.67 = 996 \]

### Final Answer
The original selling price of the article is Rs. 996.

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