Let's break this problem down step by step.

1. The shopkeeper initially marks the price of the article.
2. Then, the shopkeeper offers a 10% discount on the marked price.
3. After applying the discount, the shopkeeper sells the article and makes a 17% profit.

Let's assume the cost price of the article is "C" (in any currency unit). The shopkeeper marks the price as "M" and offers a 10% discount. Therefore, the selling price after the discount is 90% of the marked price:

Selling Price (after discount) = 0.90 * M

Now, we know that the shopkeeper makes a 17% profit on the cost price. So, the selling price is 117% of the cost price:

Selling Price (after discount) = 117% of Cost Price 0.90 * M = 1.17 * C

Now, we can solve this equation for the cost price "C" in terms of the marked price "M":

C = (0.90 * M) / 1.17

C = (90/117) * M

C = (10/13) * M

Now that we have the cost price "C" in terms of the marked price "M," we can find the profit percentage when the article is sold at the market price (without any discount). The profit percentage is calculated as:

Profit Percentage = [(Selling Price - Cost Price) / Cost Price] * 100

When the article is sold at the market price, the selling price is equal to the marked price (M):

Profit Percentage = [(M - C) / C] * 100

Substitute the expression for "C" in terms of "M":

Profit Percentage = [(M - (10/13) * M) / ((10/13) * M)] * 100

Simplify the expression:

Profit Percentage = [(3/13) * M / ((10/13) * M)] * 100

Profit Percentage = (3/10) * 100

Profit Percentage = 30%

So, the profit percentage when the article is sold at the market price (without any discount) is 30%.