Percents

[EmanueleB476]

Hi Everyone,
I think I am missing something. For the following question:

"One sell a product at 20% discount and still makes a profit of 20% of the cost. What % of the cost would the profit on the product have been if it had been sold with full price?"

Why can't I assume... (pick numbers)...
100$ original price -> 80$ discounted price -> the profit is 16$. So with original price I have 20$ more and then my 16$, that makes 36$/100$ or 36%.
But.... the answer is not 36%, instead 50%.

Where is my mistake?
Thank you very much in advance!
Best,

Manu

[Sage Pearce-Higgins]

Picking an example (Smart Numbers) is a great strategy here. Sure, let's say that the product costs $100, and it's discounted by $80. However, be careful here, we're told that it "still makes a profit of 20% of the cost". So the profit isn't 20% of $80, but 20% of the cost. We could make an equation that 1.2 x C = 80. That makes C = 200/3 = $66.67. The question asks "What % of the cost would the profit on the product have been if it had been sold with full price". We know that the full price is $100, and the cost is $66.67, so that the profit is $33.33. So the profit is ($33.33/$66.67) x 100% = 50%