The cost price of article A is ₹ 500 more than the cost price of article B. Article A is sold at a loss of 10% and B is sold at a profit of 20%. If there is a profit of ₹200 in the entire transaction, then the cost price of article A is :

Correct option is A

​$$\textbf{Given:} \\\text{Cost price of article A is } 500 \text{ more than article B} \\\text{Article A is sold at } 10\% \text{ loss} \\\text{Article B is sold at } 20\% \text{ profit} \\\text{Net profit} = 200 \\\textbf{Concept Used:} \\\text{Profit and loss with linear equations} \\\textbf{Formula Used:} \\\text{Selling Price} = \text{Cost Price} \times \left(1 \pm \frac{\text{Percentage}}{100}\right) \\\textbf{Solution:} \\\text{Let cost price of article B} = x \\\text{Then cost price of article A} = x + 500 \\\text{Selling price of A at } 10\% \text{ loss:} \\\text{SP}_A = 0.9(x + 500) \\\text{Selling price of B at } 20\% \text{ profit:} \\\text{SP}_B = 1.2x \\\text{Total selling price} = \text{Total cost price} + 200 \\0.9(x + 500) + 1.2x = (x + 500) + x + 200 \\0.9x + 450 + 1.2x = 2x + 700 \\2.1x + 450 = 2x + 700 \\2.1x - 2x = 700 - 450 \\0.1x = 250 \\x = 2500 \\\text{Cost price of article A} = x + 500 \\= 2500 + 500 \\= 3000 \\\textbf{Final Answer:} \\3000$$​​