"per cent" means simply "per hundred". That means that if 20% of your monthly budget is on food, then you buy $20 of food for every $100 you earn.
When working out profit, it works the same way, but there is a twist to it.
In your question, you are asked what price you should sell a product for if you want to make 55% profit when it costs you $1.20.
Another way of phrasing it is this: You sell a product and keep 55% of the selling price and spend the rest (45%) on your production cost. In this case 45% of that selling price equals $1.20. If you use algebra, then call the selling price P and:
P(45%) = $1.20
If you divide by (45%) on both sides, then it cancels on the left side and you have:
P = $1.20 / (45%)
Remember that percentages are just amounts "per hundred". So 45% = 45 / 100 = 0.45.
P = $1.20 / 0.45 = $2.67
So the selling price should be $2.67 if you want 55% profit on an item that costs you $1.20 to make.
Hope this helps,
Stephen La Rocque.