The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 20% profit?

Let's solve this step by step:

Step 1: Let's assume the cost price of the article is Rs. x.

Step 2: According to the problem, the percentage profit earned by selling the article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280.

This can be written as: (1920 - x)/x = (x - 1280)/x

Step 3: Solving the above equation, we get: 1920 - x = x - 1280

Step 4: Simplifying, we get: 2x = 3200

Step 5: Solving for x, we get: x = 3200 / 2 = Rs. 1600

So, the cost price of the article is Rs. 1600.

Step 6: Now, we need to find the selling price to make a 20% profit.

Profit is calculated as: Profit = Selling price - Cost price

But we want a 20% profit, so we can write this as: Selling price = Cost price + 20% of cost price

Step 7: Substituting the cost price into the equation, we get: Selling price = 1600 + 20% of 1600 Selling price = 1600 + 320 = Rs. 1920

So, to make a 20% profit, the article should be sold for Rs. 1920.