If the cost price of $20$ articles is equal to the selling price of $25$ articles, what is the $\%$ profit or $\%$ loss made by the merchant?

Let the cost price of one article be 1, making the cost price of 20 articles equal to 20. Since the cost price of 20 articles equals the selling price of 25 articles, the selling price of one article is 20 divided by 25 which is 0.8. Using the loss percent formula, Loss equals Cost Price minus Selling Price, the loss is 1 minus 0.8 equals 0.2. The loss percent is 0.2 divided by 1 times 100, which is 20 percent. The merchant incurs a 20 percent loss.

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