Understanding the Single Discount Equivalent to Two Successive Discounts of 10% and 20%: A Comprehensive Guide

Introduction

When dealing with pricing and discounts, it is often necessary to understand the concept of the single discount equivalent to two successive discounts. This article aims to elucidate the mathematical principles behind such calculations and provide a step-by-step breakdown to help you grasp the concept more intuitively.

Calculating the Single Discount

Let's consider an item with a marked price of 100 units. We will apply two successive discounts: 10% and 20%.

Step 1: Applying the First Discount

First, we apply a 10% discount to the marked price.

Marked price (M) 100 units

After the first discount:

Price M - (10% of M) 100 - (0.10 * 100) 90 units

Step 2: Applying the Second Discount

Next, we apply a 20% discount to the new price.

Second discount on 90 units:

Discount 20% of 90 0.20 * 90 18 units

Final price after both discounts:

Price 90 - 18 72 units

Step 3: Calculating the Total Discount

Total discount Marked price - Final price

Total discount 100 - 72 28 units

Step 4: Determining the Single Discount Percentage

The single discount percentage can be calculated as:

Single discount percentage (Total discount / Marked price) * 100

Single discount percentage (28 / 100) * 100 28%

Additional Examples and Calculations

The example using a 100-unit item to illustrate this concept is instructive. Let's apply the same steps to a different scenario:

Example: 100 Units

Original price (M) 100 units

First Discount: 10%

New price after first discount: 100 - (10% of 100) 90 units

Second Discount: 20%

Second discount on 90 units: 20% of 90 18 units

New price after second discount: 90 - 18 72 units

Total discount: 100 - 72 28 units

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

Mathematical Representation

A more generalized formula to find the single discount equivalent to two successive discounts of A% and B% is:

A B - A B/100

In our example, A 10 and B 20, so:

10 20

10 20 - (10 * 20 / 100)

30 - 2 28

Practical Application

In practical terms, if an item is marked at 100 units and sold after two successive discounts of 10% and 20%, the final price would be 72 units, representing a total discount of 28 units.

This concept is crucial in retail, where understanding how discounts compound is key to pricing strategies and customer satisfaction.