If a discount of 20% is applied to a product and then another discount of 15% is applied to the reduced price, what is the overall discount percentage?

Step 1: Let's assume the original price of the product is $100 for simplicity.

Step 2: A 20% discount is applied first. So, the discount amount would be 20% of $100, which is$20. Therefore, the price after the first discount is $100 -$20 = $80.

Step 3: Then, a 15% discount is applied to the reduced price of $80. So, the discount amount would be 15$80, which is $12. Therefore, the price after the second discount is$80 - $12 =$68.

Step 4: The overall discount is the original price minus the final price, which is $100 -$68 = $32.

Step 5: To find the overall discount percentage, we divide the overall discount by the original price and multiply by 100. So, the overall discount percentage is ($32 /$100) * 100 = 32%.

So, the overall discount percentage is 32%.

Sure, let's break down the problem step by step to find the overall discount percentage when two successive discounts are applied.

1. Initial Price: Let's assume the initial price of the product is $P$.

2. First Discount: A 20% discount is applied to the initial price.

   • The discount amount is $0.20 \times P = 0.20P$.
   • The price after the first discount is $P - 0.20P = 0.80P$.

3. Second Discount: A 15% discount is applied to the reduced price after the first discount.

   • The discount amount on the reduced price is $0.15 \times 0.80P = 0.12P$.
   • The price after the second discount is $0.80P - 0.12P = 0.68P$.

4. Overall Discount: The overall discount is the difference between the initial price and the final price.

   • The initial price is $P$.
   • The final price after both discounts is $0.68P$.
   • The overall discount amount is $P - 0.68P = 0.32P$.

5. Overall Discount Percentage: To find the overall discount percentage, we divide the overall discount amount by the initial price and multiply by 100.

   • Overall discount percentage = $\left( \frac{0.32P}{P} \right) \times 100 = 32\%$.

So, the overall discount percentage when a 20% discount is followed by a 15% discount is 32%.