Understanding percentage increase and decrease is crucial for students preparing for banking exams. These concepts frequently appear in various types of quantitative aptitude questions, and mastering them can significantly enhance problem-solving skills. This article delves into the essentials of percentage increase and decrease, providing clear explanations, engaging examples, and practical tips to help you excel in your exams.
What is Percentage Increase and Decrease?
Percentage increase refers to the rise in a value expressed as a percentage of the original value. Conversely, percentage decrease represents a reduction in value expressed as a percentage of the original amount. Both concepts are fundamental in daily life, from understanding price changes to calculating discounts and interest rates.
Formula for Percentage Increase
To calculate the percentage increase between two values, use the formula:
Percentage Increase = (New Value - Original Value) / Original Value × 100
Example of Percentage Increase Calculation
| Original Value | New Value | Percentage Increase |
|---|---|---|
| Rs 500 | Rs 600 | 20% |
Formula for Percentage Decrease
To determine the percentage decrease between two values, apply the formula:
Percentage Decrease = (Original Value - New Value) / Original Value × 100
Example of Percentage Decrease Calculation
| Original Value | New Value | Percentage Decrease |
|---|---|---|
| Rs 800 | Rs 600 | 25% |
Practical Applications of Percentage Increase and Decrease
Understanding how to calculate percentage changes is not only crucial for exams but also for real-world applications. Here are some common scenarios:
1. Price Adjustments
When shopping, percentage increase and decrease help determine sales prices or discounts. For instance, if a store offers a 15% discount on a Rs 1000 item, the new price is:
| Original Price | Discount Percentage | Discount Amount | New Price |
|---|---|---|---|
| Rs 1000 | 15% | Rs 150 | Rs 850 |
Further Example: If an item’s price is reduced from Rs 1200 to Rs 900, the percentage decrease is:
| Original Price | Reduced Price | Percentage Decrease |
|---|---|---|
| Rs 1200 | Rs 900 | 25% |
2. Interest Rates
In finance, percentage changes help compute interest rates and returns on investments. For example, if an investment grows from Rs 10000 to Rs 12000, the percentage increase in the value is:
| Original Value | New Value | Percentage Increase |
|---|---|---|
| Rs 10000 | Rs 12000 | 20% |
Further Example: If the value of a bond decreases from Rs 15000 to Rs 12000, the percentage decrease is:
| Original Value | New Value | Percentage Decrease |
|---|---|---|
| Rs 15000 | Rs 12000 | 20% |
3. Population Growth
In demographic studies, percentage increase helps analyze population growth. If a city’s population rises from 500,000 to 600,000, the percentage increase is:
| Original Population | New Population | Percentage Increase |
|---|---|---|
| 500,000 | 600,000 | 20% |
Further Example: If a village’s population grows from 10,000 to 12,500, the percentage increase is:
| Original Population | New Population | Percentage Increase |
|---|---|---|
| 10,000 | 12,500 | 25% |
Advanced Applications
Beyond basic examples, percentage increase and decrease have more complex applications in various fields.
1. Compound Interest
In compound interest calculations, the percentage change is not straightforward as it involves multiple periods. For instance, if an investment of Rs 5000 grows to Rs 8000 over three years, the overall percentage increase is:
| Original Value | Final Value | Percentage Increase |
|---|---|---|
| Rs 5000 | Rs 8000 | 60% |
To find the annual compound interest rate, more advanced formulas and calculations are required, typically involving logarithms.
2. Economic Indicators
In economics, percentage changes are used to measure inflation rates, GDP growth, and other economic indicators. For example, if a country’s GDP grows from Rs 2 trillion to Rs 2.5 trillion, the percentage increase in GDP is:
| Original GDP | New GDP | Percentage Increase |
|---|---|---|
| Rs 2 trillion | Rs 2.5 trillion | 25% |
3. Real Estate
In real estate, understanding percentage changes helps assess property value fluctuations. If a property’s value increases from Rs 3 million to Rs 3.6 million, the percentage increase is:
| Original Value | New Value | Percentage Increase |
|---|---|---|
| Rs 3 million | Rs 3.6 million | 20% |
Practical Tips for Calculating Percentage Increase and Decrease
While the formulas for percentage increase and decrease are straightforward, applying them efficiently can sometimes be challenging. Here are some practical tips and tricks to simplify the process using fractions:
1. Converting Percentage to Fraction
Before performing calculations, it’s often helpful to convert percentages to fractions. This makes arithmetic operations easier without relying on decimals. To convert a percentage to a fraction, divide the percentage by 100 and simplify, if possible. For example:
- 15% as a fraction is 15/100 = 3/20
- 25% as a fraction is 25/100 = 1/4
2. Calculating Percentage Increase and Decrease Using Fractions
When dealing with percentage increase or decrease, you can use the following method with fractions:
Percentage Increase:
To find the new value after a percentage increase, multiply the original value by 1 + (percentage in fraction form). For example, to increase Rs 500 by 20%:
- Convert 20% to a fraction: 1/5
- Add this fraction to 1: 1 + 1/5 = 6/5
- Multiply the original value: 500 × 6/5 = 3000/5 = 600
So, after increasing Rs 500 by 20%, the new value is Rs 600.
| Original Value | Percentage Increase | New Value Calculation | New Value |
|---|---|---|---|
| Rs 500 | 20% | Rs 500 × 6/5 = 600 | Rs 600 |
Percentage Decrease:
To find the new value after a percentage decrease, multiply the original value by 1 – (percentage in fraction form). For instance, to decrease Rs 800 by 25%:
- Convert 25% to a fraction: 1/4
- Subtract this fraction from 1: 1 – 1/4 = 3/4
- Multiply the original value: 800 × 3/4 = 2400/4 = 600
So, after decreasing Rs 800 by 25%, the new value is Rs 600.
| Original Value | Percentage Decrease | New Value Calculation | New Value |
|---|---|---|---|
| Rs 800 | 25% | Rs 800 × 3/4 = 600 | Rs 600 |
3. Working with Multiple Percentage Changes
When dealing with multiple percentage changes, such as successive increases or decreases, apply each percentage change step by step. For example, if a value increases by 10% and then by another 5%, calculate each step:
| Original Value | First Increase | Second Increase | Final Value |
|---|---|---|---|
| Rs 1000 | Rs 1000 × 11/10 = 1100 | Rs 1100 × 21/20 = 1155 | Rs 1155 |
4. Using Reverse Calculations
Sometimes, you might need to reverse-engineer a percentage problem. For instance, if you know the final value after an increase and need to find the original value:
Finding Original Value After Increase:
Divide the final value by 1 + (percentage in fraction form). For example, if Rs 1200 is 20% more than the original value:
| Final Value | Percentage Increase | Original Value Calculation | Original Value |
|---|---|---|---|
| Rs 1200 | 20% | Rs 1200 ÷ 6/5 = Rs 1000 | Rs 1000 |
Finding Original Value After Decrease:
Divide the final value by 1 – (percentage in fraction form). For instance, if Rs 750 is 25% less than the original value:
| Final Value | Percentage Decrease | Original Value Calculation | Original Value |
|---|---|---|---|
| Rs 750 | 25% | Rs 750 ÷ 3/4 = Rs 1000 | Rs 1000 |
Conclusion
By mastering these practical tips for calculating percentage increase and decrease using fractions, you can approach problems with greater confidence and accuracy. These methods are crucial for banking exams and real-world financial scenarios. Practicing these techniques regularly will sharpen your skills and help you solve percentage problems efficiently.
Remember, understanding the fundamental principles and applying these methods will enhance both your exam performance and daily decision-making involving percentage calculations.