1. **State the problem:** We need to find the discount percentage when the original price of a couch is 405 and the discounted price is 162. 2. **Formula for discount percentage:** $$\text{Discount Percentage} = \frac{\text{Original Price} - \text{Discounted Price}}{\text{Original Price}} \times 100\%$$ 3. **Calculate the discount amount:** $$405 - 162 = 243$$ 4. **Substitute values into the formula:** $$\text{Discount Percentage} = \frac{243}{405} \times 100\%$$ 5. **Simplify the fraction:** $$\frac{243}{405} = \frac{\cancel{81} \times 3}{\cancel{81} \times 5} = \frac{3}{5}$$ 6. **Calculate the percentage:** $$\frac{3}{5} \times 100\% = 60\%$$ **Final answer:** The discount percentage is **60%**.