Sum of Ages
Sum of Ages problems provide the total sum of ages of two or more persons. These problems often combine sum information with other relationships like ratios or differences to find individual ages.
What You'll Learn
Introduction to Sum of Ages
Sum of Ages problems provide the total sum of ages of two or more persons. These problems often combine sum information with other relationships like ratios or differences to find individual ages.
Prerequisites
How to Solve Sum of Ages Problems
Step 1: Identify all persons whose ages are to be summed
Step 2: Write the sum equation: Age1 + Age2 + ... = Total
Step 3: Express each age in terms of a single variable if relationships exist
Step 4: Substitute into the sum equation
Step 5: Solve for the variable
Step 6: Calculate individual ages
Step 7: Verify that the sum matches the given total
Example Problem
Example: The sum of ages of A and B is 50 years. A is 10 years older than B. Find their ages. Solution: Step 1: Let B = x, then A = x + 10 Step 2: Sum: (x + 10) + x = 50 Step 3: 2x + 10 = 50 → 2x = 40 → x = 20 Step 4: B = 20, A = 30 years Answer: A = 30, B = 20 years
Pro Tips & Tricks
- Sum = Age1 + Age2 + ...
- If ages are in ratio a:b, then sum = k(a+b)
- If one person is x years older, express the older as younger + x
- For three or more persons, systematically reduce variables
- The average age = Sum ÷ Number of persons
- Future sum = Present sum + (n × number of persons)
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Sum of Ages. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Sum of Ages is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Sum of Ages?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: