Percentage Increase/Decrease Calculations

Percentage Increase/Decrease Calculations

Percentages are essential in various fields, including finance, economics, and statistics, where they allow for easy comparisons and analyses of changes. In mathematics, learning to calculate percentage increases and decreases is crucial. This article aims to explain the calculation and examples of percentage increases and decreases.

Understanding Percentages

A percentage is a measure representing the part of a whole. It is calculated as a fraction of 100. For instance, if Suresh's annual salary increased from Rs 18,00,000 to Rs 22,00,000, the percentage increase would be calculated as follows:

(Increase / Original value) * 100 = 22.22%

Similarly, if the population of a small town decreased from 18,560 to 15,787 due to an epidemic, the percentage decrease could be found using the following formula:

(Decrease / Original value) * 100 = 14.94%

These formulas allow us to determine the percentage change in a quantity over time.

Calculating Percentage Increases

To calculate percentage increases, follow these steps:

1. Determine the difference between the original value and the increased value.
2. Divide the difference by the original value.
3. Multiply the quotient obtained in step 2 by 100.

For example, let's consider the scenario mentioned earlier: Suresh's annual salary increased from Rs 18,00,000 to Rs 22,00,000. Here, the difference is Rs 4,00,000, which can be calculated as Rs 22,00,000 – Rs 18,00,000. Next, divide this difference by the original salary, Rs 18,00,000:

(Rs 4,00,000 / Rs 18,00,000) = 0.2222

Now, multiply 0.2222 by 100 to get the percentage increase:

0.2222 * 100 = 22.22%

So, Suresh's annual salary increased by 22.22%.

Calculating Percentage Decreases

To calculate percentage decreases, the process remains the same, but we focus on the decrease in value instead. Follow these steps:

1. Determine the difference between the original value and the decreased value.
2. Divide the difference by the original value.
3. Multiply the quotient obtained in step 2 by 100.

For instance, let's revisit the scenario mentioned earlier: the population of a small town decreased from 18,560 to 15,787 due to an epidemic. Here, the decrease is 2773, which can be calculated as 18,560 – 15,787. Next, divide this difference by the original population, 18,560:

(2773 / 18,560) = 0.1494

Now, multiply 0.1494 by 100 to get the percentage decrease:

0.1494 * 100 = 14.94%

So, the population decreased by 14.94%.

These formulas and methods enable us to calculate percentage increases and decreases accurately and provide valuable insights into changes in quantities over time.