Percentage Change: How to Determine and Interpret It

Percentage Change: How to Determine and Interpret It

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Introduction

Welcome to today’s lesson on percentages! Understanding percentage change is a fundamental concept in quantitative aptitude, especially for banking and finance-related exams. Percentage change helps us compare how much a value has increased or decreased in relation to its original value. In this article, we will break down the concept of percentage change in a clear, step-by-step manner, providing practical examples and exercises to enhance your learning.

What is Percentage Change?

Percentage change is a measure that expresses the amount of increase or decrease of a quantity as a percentage of its original value. It is commonly used in various fields such as finance, economics, and statistics to analyze trends over time.

Formula for Calculating Percentage Change

The formula to calculate percentage change is:

Percentage Change = (New Value – Old Value) / Old Value × 100

Where:

  • New Value: The value after the change has occurred.
  • Old Value: The value before the change occurred.

Step-by-Step Guide to Calculate Percentage Change

  1. Identify the Old Value and New Value: Begin by determining the original (old) value and the value after the change (new value).
  2. Subtract the Old Value from the New Value: This will give you the difference between the two values:Difference = New Value – Old Value
  3. Divide the Difference by the Old Value: This step helps to find the relative change in value:Relative Change = Difference / Old Value
  4. Multiply by 100 to Get the Percentage: Finally, to convert the relative change into a percentage, multiply by 100:Percentage Change = Relative Change × 100

Using Fractions to Calculate Percentage Change

When we use fractions, we can maintain accuracy without introducing decimals. Here’s how:

  1. Calculate the Difference Using Fractions: Suppose our old value is represented as a and the new value as b:Difference = b – a
  2. Express Relative Change as a Fraction:Relative Change = (b – a) / a
  3. Convert to Percentage:Percentage Change = (b – a) / a × 100

Practical Examples

Example 1: Increase in Value

Suppose the price of a smartphone increased from Rs 15,000 to Rs 18,000. To find the percentage change:

  • Old Value = Rs 15,000
  • New Value = Rs 18,000
  1. Calculate the Difference:Difference = 18,000 – 15,000 = 3,000
  2. Express the Old Value as a Fraction:The old value can be represented as Rs 15,000 or 15,000/1.
  3. Calculate Relative Change:Relative Change = 3,000 / 15,000 = 3 / 15 = 1 / 5
  4. Convert to Percentage:Percentage Change = (1/5) × 100 = 20%

The price of the smartphone increased by 20%.

Example 2: Decrease in Value

Now, let’s say the price of a laptop decreased from Rs 40,000 to Rs 35,000. To find the percentage change:

  • Old Value = Rs 40,000
  • New Value = Rs 35,000
  1. Calculate the Difference:Difference = 35,000 – 40,000 = -5,000
  2. Express the Old Value as a Fraction:The old value is Rs 40,000 or 40,000/1.
  3. Calculate Relative Change:Relative Change = -5,000 / 40,000 = -5 / 40 = -1 / 8
  4. Convert to Percentage:Percentage Change = (-1/8) × 100 = -12.5%

The price of the laptop decreased by 12.5%.

Interpreting Percentage Change

Understanding the outcome of your calculations is as important as performing the calculations themselves. A positive percentage indicates an increase, while a negative percentage signifies a decrease. This information is vital for making informed decisions in various contexts, such as budgeting, investments, and analyzing sales data.

Applications of Percentage Change

Percentage change is widely applicable in daily life and various fields:

  • Finance: To assess changes in stock prices or interest rates.
  • Economics: To evaluate inflation rates or changes in GDP.
  • Sales and Marketing: To determine sales growth or decline over specific periods.

Common Mistakes to Avoid

While calculating percentage change, keep these common pitfalls in mind:

  • Forgetting to specify whether the change is an increase or decrease.
  • Not using the original value for calculations, leading to inaccurate percentages.
  • Confusing percentage change with absolute change (which does not take the original value into account).

Exercises for Practice

To reinforce your understanding of percentage change, here are 15 practice exercises. Try solving them using the steps outlined in this article:

  1. The population of a town increased from 25,000 to 30,000. What is the percentage change?
  2. A jacket was priced at Rs 2,000 and is now Rs 1,600. What is the percentage decrease?
  3. The weight of a package decreased from 50 kg to 45 kg. Calculate the percentage change.
  4. A stock price went from Rs 200 to Rs 250. Find the percentage increase.
  5. An employee’s salary dropped from Rs 60,000 to Rs 54,000. What is the percentage decrease?
  6. A company’s profit increased from Rs 1,00,000 to Rs 1,50,000. Find the percentage increase.
  7. The cost of a TV went from Rs 60,000 to Rs 54,000. What is the percentage change?
  8. A car’s price fell from Rs 500,000 to Rs 450,000. Calculate the percentage decrease.
  9. The attendance in a school increased from 200 to 250 students. What is the percentage change?
  10. A gym membership fee decreased from Rs 2,500 to Rs 2,000. Calculate the percentage decrease.
  11. A restaurant’s revenue increased from Rs 2,00,000 to Rs 2,50,000. What is the percentage increase?
  12. The temperature rose from 20°C to 25°C. Calculate the percentage change in temperature.
  13. A mobile phone’s price reduced from Rs 30,000 to Rs 25,000. Find the percentage decrease.
  14. The sales of a product increased from Rs 10,000 to Rs 15,000. Calculate the percentage increase.
  15. A real estate property’s value decreased from Rs 80,000 to Rs 70,000. What is the percentage decrease?

Answers to Practice Questions

  1. Percentage Change = (30,000 – 25,000) / 25,000 × 100 = 20%
  2. Percentage Decrease = (2,000 – 1,600) / 2,000 × 100 = 20%
  3. Percentage Change = (45 – 50) / 50 × 100 = -10%
  4. Percentage Increase = (250 – 200) / 200 × 100 = 25%
  5. Percentage Decrease = (60,000 – 54,000) / 60,000 × 100 = 10%
  6. Percentage Increase = (1,50,000 – 1,00,000) / 1,00,000 × 100 = 50%
  7. Percentage Change = (54,000 – 60,000) / 60,000 × 100 = -10%
  8. Percentage Decrease = (500,000 – 450,000) / 500,000 × 100 = 10%
  9. Percentage Change = (250 – 200) / 200 × 100 = 25%
  10. Percentage Decrease = (2,500 – 2,000) / 2,500 × 100 = 20%
  11. Percentage Increase = (2,50,000 – 2,00,000) / 2,00,000 × 100 = 25%
  12. Percentage Change = (25 – 20) / 20 × 100 = 25%
  13. Percentage Decrease = (30,000 – 25,000) / 30,000 × 100 = 16.67%
  14. Percentage Increase = (15,000 – 10,000) / 10,000 × 100 = 50%
  15. Percentage Decrease = (80,000 – 70,000) / 80,000 × 100 = 12.5%

Conclusion

Understanding percentage change is a valuable skill that can help you in various aspects of life, from managing personal finances to interpreting market trends. By mastering the calculation of percentage change using fractions, you can ensure greater accuracy and clarity in your work. Practice regularly, and you’ll find yourself becoming more comfortable with this essential mathematical concept.

 

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