Understanding the concept of increasing or decreasing a quantity, X, by a certain percentage, P%, is crucial in various fields, including finance, statistics, and everyday calculations. This comprehensive guide breaks down the process into understandable steps, making you proficient in performing these calculations effortlessly.
Understanding the Basics
Definitions:
- X: The original number or value.
- P%: The percentage by which the original number, X, is increased or decreased.
Key Concepts:
- Increase: To add a certain percentage to the original number, making it larger.
- Decrease: To subtract a certain percentage from the original number, making it smaller.
The Mathematical Approach
Increasing X by P%
To increase a number by a certain percentage:
- Convert the percentage (P%) into a decimal by dividing by 100.
- Multiply the original number (X) by the decimal equivalent of the given percentage.
- Add the result from step 2 to the original number (X) to find the new value.
Formula: New Value = X + (X * (P/100))
Decreasing X by P%
To decrease a number by a certain percentage:
- Convert the percentage (P%) into a decimal by dividing by 100.
- Multiply the original number (X) by the decimal equivalent of the given percentage.
- Subtract the result from step 2 from the original number (X) to find the new value.
Formula: New Value = X – (X * (P/100))
Practical Examples
Example 1: Increasing a Value
Question: What is 200 increased by 10%?
Solution:
- Convert 10% to decimal: 10/100 = 0.1
- Calculate 10% of 200: 200 * 0.1 = 20
- Add the result to the original number: 200 + 20 = 220
Answer: 200 increased by 10% is 220.