Understanding Successive Discounts and Their Equivalence

When dealing with pricing and sales in a business environment, understanding successive discounts is crucial. A common question arises: What is the equivalent single discount when two or more successive discounts are applied? This article aims to clarify this concept with detailed calculations and examples.

Overview of Successive Discounts

Successive discounts, also known as chain discounts, apply a series of discounts consecutively on a product's original price. To calculate the single equivalent discount, we need to consider how each discount impacts the final price.

Calculating Single Equivalent Discount

Let's start with an example where the original price is 100 Units.

Example 1: 20% followed by 10%

1. Apply the first discount of 20%:

Original price: 100 Units

First discount: 20% of 100 20 Units

Remaining amount: 100 - 20 80 Units

2. Apply the second discount of 10% on the remaining amount:

Second discount: 10% of 80 8 Units

Final amount: 80 - 8 72 Units

3. Calculate the single equivalent discount:

Total discount: 100 - 72 28 Units

Single equivalent discount: (28 / 100) * 100% 28%

Example 2: 10% followed by 5% followed by 10%

1. Apply the first discount of 10%:

Original price: 100 Units

First discount: 10% of 100 10 Units

Remaining amount: 100 - 10 90 Units

2. Apply the second discount of 5% on the remaining amount:

Second discount: 5% of 90 4.5 Units

Remaining amount: 90 - 4.5 85.5 Units

3. Apply the third discount of 10% on the remaining amount:

Third discount: 10% of 85.5 8.55 Units

Final amount: 85.5 - 8.55 76.95 Units

4. Calculate the total discount:

Total discount: 100 - 76.95 23.05 Units

Single equivalent discount: (23.05 / 100) * 100% 23.05%

Real-World Application

In practical scenarios, the distribution of successive discounts can vary based on the promotional schedule. For example, a distributor might offer a 20% discount for the first 4 weeks, a 10% discount for the next 3 weeks, and a 5% discount for the final week. The single equivalent discount can only be accurately calculated if the exact dates of application are known.

Example 3: 20% for 4 weeks, 10% for 3 weeks, and 5% for 1 week

1. Apply the first discount of 20%:

Original price: 100 Units

First discount: 20% of 100 20 Units

Remaining amount: 100 - 20 80 Units

2. Apply the second discount of 10% on the remaining amount:

Second discount: 10% of 80 8 Units

Remaining amount: 80 - 8 72 Units

3. Apply the third discount of 5% on the remaining amount:

Third discount: 5% of 72 3.6 Units

Final amount: 72 - 3.6 68.40 Units

4. Calculate the total discount:

Total discount: 100 - 68.4 31.6 Units

Single equivalent discount: (31.6 / 100) * 100% 31.6%

Conclusion

Understanding successive discounts and their equivalent single rates is essential for businesses to accurately price their products and manage sales strategies. By following the calculations provided, you can ensure that your pricing is competitive and aligned with market expectations.