1. **Problem statement:** A shopkeeper raises the price of a product by 50% on the cost price. We need to find the discount percentage on the marked price so that the shopkeeper still makes a 20% profit. 2. **Define variables:** Let the cost price be $C$. 3. **Calculate marked price (MP):** The shopkeeper raises the price by 50%, so $$MP = C + 0.5C = 1.5C$$ 4. **Calculate selling price (SP) for 20% profit:** To get a 20% profit on cost price, $$SP = C + 0.2C = 1.2C$$ 5. **Find discount given:** Discount is the difference between marked price and selling price, $$\text{Discount} = MP - SP = 1.5C - 1.2C = 0.3C$$ 6. **Calculate discount percentage on marked price:** $$\text{Discount \%} = \frac{\text{Discount}}{MP} \times 100 = \frac{0.3C}{1.5C} \times 100 = 20\%$$ **Final answer:** The discount percentage is **20%**.