A trader sold an article, after giving a discount which was 20% of the selling price, for a profit of 20% which is calculated on the selling price. If he had sold the article at the marked price, what would his profit percentage have been?

Let's break this down:

1. The trader sold an article after giving a 20% discount on the selling price. This means the selling price is 80% of the marked price. Let's denote the marked price as MP and the selling price as SP. So, SP = 0.8 * MP.

2. The trader made a profit of 20% on the selling price. This means the cost price (CP) of the article is 80% of the selling price. So, CP = 0.8 * SP.

3. If the trader had sold the article at the marked price, his profit would have been MP - CP.

4. The profit percentage is calculated as (Profit / CP) * 100.

Now, let's substitute the values:

1. From step 1, we know SP = 0.8 * MP. So, MP = SP / 0.8.

2. From step 2, we know CP = 0.8 * SP.

3. From step 3, the profit if sold at marked price would be MP - CP = (SP / 0.8) - (0.8 * SP).

4. The profit percentage would then be {[(SP / 0.8) - (0.8 * SP)] / (0.8 * SP)} * 100.

Solving this equation gives the profit percentage as 25%. So, if the trader had sold the article at the marked price, his profit percentage would have been 25%.