Easy way:

Let x = original selling price of item

Let c = cost of the item

0.8x = 1.2c ---> x = (1.2/0.8)c = 1.5c ====> 50% profit ----> Answer Choice C


Explanation:

We are told that the selling price of an item is reduced by 20%, but it is still sold at a profit of 20% of the cost of the item. That means:

(1-0.2)(selling price - cost) / cost = 0.2 --------> 0.8(selling price - cost) / cost = 0.2

0.8(selling price - cost) = 0.2 (cost) --------> 0.8(selling price) = 1.2 (cost) =====> selling price = (1.2/0.8) cost = 1.5 (cost)


Reverse the process:

selling price - cost = 0.5 (cost) ------> (selling price - cost) / cost = 0.5 ====> a profit that is 50% of the cost