A shop owner needs to make a 20% profit on a particular

BTGmoderatorLU wrote:A shop owner needs to make a 20% profit on a particular item that cost him $20. He wants to give a 20% discount on the retail price and still net the 20% profit. At what retail price should be set the item?

A. $24.00
B. $28.00
C. $28.80
D. $30.00
E. $32.60

The OA is D.

Cost price = 20
Profit to be made = 20%
Therefore, selling price = 20*1.2 = 24

Let the retail price = x
Discount of 20% on retail price, implies the new selling price should be = 0.8x
But this is = 20% profit of cost price, which is same as selling price of 24
Therefore, 0.8x = 24

Hence, retail price = 24/0.8 = 30. Option D.

Please, can anyone explain another way to solve this PS question? Thanks!

Hi BTGmoderatorLU.

I think your approach is the best but you also could solve it as follows:

Let be:
- Pc the cost price ($20).
- Pr the retail price.

1. The owner wants to make a 20% profit on Pc, this implies that he should sell the item at 120%Pc.

2. Since the owner wants to make a 20% discount on the retail price, then the retail price after the discount is equal to 80%Pr.

Now, 1 and 2 have to represent the same, hence $$120\%\cdot P_c=80\%\cdot P_r$$ $$\Leftrightarrow\ \ P_r=\frac{120\%}{80\%}\cdot P_c$$ $$\Leftrightarrow\ \ P_r=\frac{3}{2}\cdot P_c$$ $$\Leftrightarrow\ \ P_r=\frac{3}{2}\cdot20=30.$$ This tells us that the retail price must be $30 in order to offer the 20% discount and still get the 20% profit.

Hence, the correct answer is the option D .

I hope it helps.