An article was sold at a loss of 15%. If it was sold for Rs.1,035 more, then there would have been a profit of 8%. Find the cost price of the article.

Options

A. A)4000
B. B)4200
C. C)4500
D. D)3500

Answer

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

### Step 1: Define the Cost Price (CP)
Let the cost price of the article be \( CP \).

### Step 2: Calculate Selling Price at a Loss
The article was sold at a loss of 15%. Therefore, the selling price (SP1) can be calculated as:
\[ SP1 = CP - (15\% \text{ of } CP) = CP \times (1 - 0.15) = CP \times 0.85 \]

### Step 3: Calculate Selling Price at a Profit
If the article was sold for Rs. 1,035 more, it would have resulted in a profit of 8%. Thus, the new selling price (SP2) can be expressed as:
\[ SP2 = CP + (8\% \text{ of } CP) = CP \times (1 + 0.08) = CP \times 1.08 \]

### Step 4: Set Up the Equation
According to the problem, the difference between SP2 and SP1 is Rs. 1,035. Therefore, we can write the equation:
\[ SP2 - SP1 = 1035 \]
Substituting the expressions for SP1 and SP2:
\[ (CP \times 1.08) - (CP \times 0.85) = 1035 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ CP \times (1.08 - 0.85) = 1035 \]
\[ CP \times 0.23 = 1035 \]

### Step 6: Solve for Cost Price (CP)
To find the cost price, divide both sides by 0.23:
\[ CP = \frac{1035}{0.23} \]
Calculating this gives:
\[ CP = 4500 \]

### Conclusion
The cost price of the article is Rs. 4,500.

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