Problem Solving

For questions involving profit, should we always consider three trpes of variables? Original Cost, Market Price and Selling Price? Here is one of those questions,

A merchant sells an item at a 20% discount, but still makes a gross profit of 20% of the cost. Whta percent of the cost would the gross profit on the item have been if it had been sold without the discount?
1. 20% 2. 40% 3. 50% 4. 60% 5. 75%

I made the mistake of taking the discount off the "cost" as well as the increase in the profit of the "cost". I wanted to make sure I understannd the concept with these kind of "profit" questions.

Answer is 50%.

Use 100 as original retail price
After discount price= 80

cost*1.2=80
cost= 80/1.2= 200/3=66.6

If sold at 100 profit will be= 100-200/3= 100/3=33.3

Profit % if sold at original price= (33.3/66.6)*100= 50%

I suggest in such case sstart with 100 and move from there onwards. makes it much easier this way