Age Ratio
Age Ratio problems give the ratio of ages of two or more persons, often along with their sum or difference. These problems require using a common multiplier to convert the ratio into actual ages.
What You'll Learn
Introduction to Age Ratio
Age Ratio problems give the ratio of ages of two or more persons, often along with their sum or difference. These problems require using a common multiplier to convert the ratio into actual ages.
Prerequisites
How to Solve Age Ratio Problems
Step 1: Write the ratio of ages in simplest form (a:b:c)
Step 2: Let the actual ages be a×k, b×k, c×k (where k is the common multiplier)
Step 3: Use the given sum or difference to form an equation
Step 4: Solve for k
Step 5: Multiply each ratio term by k to get actual ages
Step 6: Verify that ages satisfy all given conditions
Step 7: Answer the specific question asked
Example Problem
Example: The ratio of ages of A and B is 3:4. The sum of their ages is 35 years. Find their ages. Solution: Step 1: Ratio A:B = 3:4 Step 2: Let A = 3k, B = 4k Step 3: Sum = 3k + 4k = 7k = 35 Step 4: k = 35 ÷ 7 = 5 Step 5: A = 3×5 = 15 years, B = 4×5 = 20 years Answer: A = 15, B = 20 years
Pro Tips & Tricks
- Always simplify the ratio to its lowest terms first
- k = Total sum ÷ Sum of ratio terms
- For two persons: k = Sum/(a+b)
- For difference: k = Difference/|a-b|
- Individual age = Ratio term × k
- Check if ages are integers (k should divide appropriately)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Age Ratio. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Age Ratio is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Age Ratio?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: