Aman sells two articles A and B. He sells article A at a profit of 24% and article B at a loss of 12%. If the cost price ratio of articles A to B is $2:3$ and the total profit earned by Aman is Rs. 300, what is the difference between the selling prices of articles A and B?

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**Solution:**

1. Let the cost price of article A be $2x$ and article B be $3x$ as per the given ratio $2:3$.

2. Selling price of article A = Cost price + Profit = $2x + 24\%$ of $2x = 2x + 0.24 	imes 2x = 2x 	imes 1.24 = 2.48x$

3. Selling price of article B = Cost price - Loss = $3x - 12\%$ of $3x = 3x - 0.12 	imes 3x = 3x 	imes 0.88 = 2.64x$

4. Total profit = Selling price of A + Selling price of B - Total cost price

Total cost price = $2x + 3x = 5x$

Total selling price = $2.48x + 2.64x = 5.12x$

Total profit = $5.12x - 5x = 0.12x$

5. Given total profit is Rs. 300, so:

$$0.12x = 300 \implies x = \frac{300}{0.12} = 2500$$

6. Difference in selling prices = $2.64x - 2.48x = 0.16x = 0.16 	imes 2500 = 400$

**Answer:** Rs. 400

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