Everything here is a percentage of the cost price, with one exception that catches nearly everybody: discount is a percentage of the MARKED price, not of cost. Questions are built around that difference.
Write down which of the three prices - cost, marked, selling - the question gives you before you do anything else. Most errors in this topic are a correct calculation of the wrong base.
Try each one before opening the answer. A solution you have read is not a solution you can produce under time pressure, which is the only kind that counts.
Q1 An article marked at 1200 is sold at a 15% discount, and the shopkeeper still makes 20% profit. What did it cost him?
850.
Selling price = 1200 × 0.85 = 1020. That is cost plus 20%, so cost = 1020 / 1.20 = 850. Note the two different bases: the discount is off 1200, the profit is on 850.
Q2 Two radios are sold for 990 each. One gives a 10% profit and the other a 10% loss. What is the overall result?
A loss of 20, which is 1% of the total cost.
The first cost 990/1.1 = 900, the second 990/0.9 = 1100. Total cost 2000, total received 1980, so a loss of 20. The shortcut: equal selling prices at ±x% always lose x²/100 per cent, here 100/100 = 1%.
Q3 A dishonest trader sells goods at cost price but uses a weight of 800 g in place of a kilogram. What is his profit percentage?
25%.
He pays for 800 g and charges for 1000 g. The gain is 200 g on an outlay of 800 g, which is 200/800 = 25%. Dividing by 1000 instead - giving 20% - is the usual wrong answer, and it is wrong because profit is measured against what he spent.