Given:
- There is a loss of 12.5% when the article is sold at half of the previous selling price.

To find:
- The percentage profit after selling an article at a certain price.

Explanation:
Let's assume the original selling price of the article to be 'x'.

According to the given information, when the article is sold at half of the previous selling price, the new selling price becomes x/2. And there is a loss of 12.5% when the article is sold at this price.

Therefore, the selling price at which there is a loss of 12.5% is (x/2) - (12.5% of x/2).

Calculating the selling price with a loss of 12.5%:
Loss % = (Loss / Cost Price) x 100

Loss % = 12.5%
Loss = (12.5/100) x (x/2) = x/16

Selling Price = Cost Price - Loss
Selling Price = (x/2) - (x/16) = (8x - x) / 16 = 7x/16

Calculating the percentage profit:
Profit % = (Profit / Cost Price) x 100

Profit % = (Selling Price - Cost Price) / Cost Price x 100

Profit % = (7x/16 - x) / x x 100 = (7x - 16x) / 16x x 100 = -9x / 16x x 100 = -9/16 x 100 = -56.25%

Since the profit percentage is negative, it means there is a loss of 56.25% when the article is sold at x/2.

Now, to find the selling price at which there will be a profit, we need to add this loss percentage to the selling price.

New Selling Price = (x/2) + (56.25% of x/2) = (x/2) + (56.25/100) x (x/2) = (x/2) + (9x/32) = (8x+9x)/32 = 17x/32

Calculating the percentage profit:
Profit % = (Selling Price - Cost Price) / Cost Price x 100

Profit % = (17x/32 - x) / x x 100 = (17x - 32x) / 32x x 100 = -15x / 32x x 100 = -15/32 x 100 = -46.875%

Again, the profit percentage is negative, which means there is a loss of 46.875% when the article is sold at 17x/32.

Since we are looking for the percentage profit, we need to find the positive value of the percentage loss.

Calculating the percentage profit:
Percentage Profit = 100 - Percentage Loss

Percentage Profit = 100 - (-46.875) = 100 + 46.875 = 146.875%

Therefore, the percentage profit after selling the article at a certain price is 146.875%.

Conclusion:
The correct answer is option C) 75%.