Introduction
Applied mathematics helps us solve real-world problems. Percentage is a vital part of this, used to compare quantities out of a base of 100.
Calculating discounts in a shop is a common use of percentages.
Explanation Step by Step
To find the percentage of a number, follow these steps: Multiply the total amount by the percentage rate, then divide by 100.
Sub-topics
Applied mathematics - Percentage
Percentages convert fractions into a standard format where the denominator is always 100.
Examples
Example 1 (Real-life)
A student scored 40 out of 50 in a test. What is the percentage?
Tricky Example
If the price of a toy increases by 10% and then decreases by 10%, is the price the same as the original?
Tricks and Shortcuts
1. To find 25%, just divide the number by 4.
2. x% of y is always equal to y% of x. (e.g., 8% of 50 is the same as 50% of 8).
Common Mistakes
1. Forgetting to divide by 100 after multiplying.
2. Calculating percentage on the wrong base value in multi-step problems.
Practice Questions
Easy Questions
- Find 20% of 200.
- A water tank is 75% full. If it holds 100 liters, how much water is in it? (Real-life)
- What is 0.5 as a percentage? (Tricky)
Medium Questions
- A shopkeeper gives a 15% discount on a 1200 rupee jacket. What is the discount amount? (Real-life)
- If 30% of a number is 90, find the number.
- Which is greater: 20% of 50 or 50% of 20? (Tricky)
Hard Questions
- The population of a town increased from 20000 to 22000. Find the percentage increase. (Real-life)
- A man spends 70% of his income and saves 9000 rupees. What is his total income? (Tricky)
- In an election, a candidate got 55% of the total valid votes. If 20% of the votes were invalid and total votes were 7500, find the valid votes the candidate got. (Tricky/Real-life)
Revision Summary
Percentage means 'per hundred'. It is used to calculate profit, loss, tax, and growth. Use the formula: (Part/Whole) × 100.