Cross Age
Cross Age problems involve interwoven relationships where multiple persons' ages are connected through cross-references (e.g., 'A is as old as B was when C was as old as D is now'). These are among the most complex age puzzles.
What You'll Learn
Introduction to Cross Age
Cross Age problems involve interwoven relationships where multiple persons' ages are connected through cross-references (e.g., 'A is as old as B was when C was as old as D is now'). These are among the most complex age puzzles.
Prerequisites
How to Solve Cross Age Problems
Step 1: Assign variables to all persons' present ages
Step 2: Identify each time shift in the statement
Step 3: Express the age at each time point as present age ± shift
Step 4: Set up equations by equating the described relationships
Step 5: Create a system of equations from all relationships
Step 6: Solve systematically, often finding relationships first
Step 7: Find individual ages using additional conditions
Example Problem
Example: A is as old as B will be when C is as old as A is now. If A is 30, find relationship between B and C. Solution: Step 1: Let B = x, C = y Step 2: When C is as old as A (30): years from now = 30 - y Step 3: At that time, B's age = x + (30 - y) Step 4: This equals A's present age (30): x + 30 - y = 30 → x - y = 0 → x = y Answer: B and C are the same age
Pro Tips & Tricks
- Start with the innermost comparison when parsing
- Use variables for time shifts (t years from now, s years ago)
- Age at time t = Present age + t (or -t for past)
- The difference between any two persons' ages is constant
- Cross-age problems often yield relationships without absolute ages
- Draw a timeline with multiple reference points
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Cross Age. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Cross Age is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Cross Age?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: