By selling an article at 7% profit Instead of 11% loss, a man gains Rs. 720 more. What is the cost price (in Rs.) of that article?

Options

A. 3200
B. 4000
C. 4800
D. 7200

Answer

To solve the problem step by step, let's denote the cost price (CP) of the article as \( x \).

### Step 1: Understand the Selling Prices
- When the article is sold at a **7% profit**, the selling price (SP1) can be calculated as:
\[ SP1 = CP + 7\% \text{ of } CP = x + 0.07x = 1.07x \]

- When the article is sold at an **11% loss**, the selling price (SP2) can be calculated as:
\[ SP2 = CP - 11\% \text{ of } CP = x - 0.11x = 0.89x \]

### Step 2: Set Up the Equation
According to the problem, the difference between the selling prices when sold at 7% profit and 11% loss is Rs. 720. Therefore, we can write the equation:
\[ SP1 - SP2 = 720 \]
Substituting the expressions for SP1 and SP2:
\[ 1.07x - 0.89x = 720 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ (1.07 - 0.89)x = 720 \]
\[ 0.18x = 720 \]

### Step 4: Solve for Cost Price (CP)
To find the cost price \( x \), divide both sides by 0.18:
\[ x = \frac{720}{0.18} \]
Calculating the right side:
\[ x = 4000 \]

### Conclusion
The cost price of the article is Rs. 4000.

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