1. Let's start by defining the problem: We want to understand how discounts affect profits and losses in a business context. 2. Suppose the original price of a product is $P$ and the cost price is $C$. 3. If a discount of $d\%$ is given, the selling price becomes $$S = P \times \left(1 - \frac{d}{100}\right)$$. 4. The profit or loss is calculated by comparing the selling price $S$ with the cost price $C$. 5. Profit if $S > C$ is $$\text{Profit} = S - C$$. 6. Loss if $S < C$ is $$\text{Loss} = C - S$$. 7. The profit or loss percentage is given by $$\text{Profit\%} = \frac{\text{Profit}}{C} \times 100$$ or $$\text{Loss\%} = \frac{\text{Loss}}{C} \times 100$$. 8. For example, if $P=200$, $C=150$, and $d=10$, then $$S = 200 \times (1 - 0.1) = 180$$. 9. Since $S=180 > C=150$, there is a profit of $$180 - 150 = 30$$. 10. The profit percentage is $$\frac{30}{150} \times 100 = 20\%$$. This shows how discounts impact profit and loss calculations in business.