Age Percentage
Age Percentage problems express age relationships using percentages (e.g., 'A is 20% older than B' or 'C's age is 75% of D's age'). These problems require converting percentages to fractions or decimals.
What You'll Learn
Introduction to Age Percentage
Age Percentage problems express age relationships using percentages (e.g., 'A is 20% older than B' or 'C's age is 75% of D's age'). These problems require converting percentages to fractions or decimals.
Prerequisites
How to Solve Age Percentage Problems
Step 1: Convert percentage statements into equations
Step 2: 'A is p% older than B' means A = B + (p/100)×B = B(1 + p/100)
Step 3: 'A is p% younger than B' means A = B - (p/100)×B = B(1 - p/100)
Step 4: 'A's age is p% of B's age' means A = (p/100)×B
Step 5: Use additional conditions (sum, difference, future/past) to solve
Step 6: Solve for the variable, typically using the k-method or fractions
Step 7: Verify the percentage relationship holds
Example Problem
Example: A is 25% older than B. The sum of their ages is 45 years. Find their ages. Solution: Step 1: A = B + 0.25B = 1.25B Step 2: A + B = 1.25B + B = 2.25B = 45 Step 3: B = 45 ÷ 2.25 = 20 years Step 4: A = 1.25 × 20 = 25 years Answer: A = 25, B = 20 years Check: A is 5 years older than B, which is 25% of 20 → 5/20 = 0.25 = 25% ✓
Pro Tips & Tricks
- p% older = multiply by (1 + p/100)
- p% younger = multiply by (1 - p/100)
- Convert percentages to fractions: 20% = 1/5, 25% = 1/4, 33.33% = 1/3
- Use fractions instead of decimals for exact calculations
- Check if percentage is of present age or another person's age
- The phrase 'percent more' indicates addition to 100%
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Age Percentage. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Age Percentage is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Age Percentage?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: