Reverse Age (Trick)
Reverse Age Trick problems involve ages where the digits reverse over time (e.g., a person's age now is the reverse of what it was n years ago). These problems test number theory and digit manipulation skills.
What You'll Learn
Introduction to Reverse Age (Trick)
Reverse Age Trick problems involve ages where the digits reverse over time (e.g., a person's age now is the reverse of what it was n years ago). These problems test number theory and digit manipulation skills.
Prerequisites
How to Solve Reverse Age (Trick) Problems
Step 1: Let the two-digit age be represented as 10a + b
Step 2: The reversed age is 10b + a
Step 3: Set up equation based on time difference
Step 4: For 'n years ago, age was reverse': (10a+b) - n = 10b + a
Step 5: Simplify: 9a - 9b = n → 9(a-b) = n
Step 6: Since n is between 1-99, a-b must be such that 9(a-b) = n
Step 7: Find possible (a,b) pairs and verify reasonableness
Example Problem
Example: A person's age now is the reverse of what it was 9 years ago. If the sum of digits is 10, find his present age. Solution: Step 1: Let present age = 10a + b Step 2: Age 9 years ago = 10b + a Step 3: (10a+b) - 9 = 10b + a Step 4: 10a + b - 9 = 10b + a → 9a - 9b = 9 → a - b = 1 Step 5: Given a + b = 10 Step 6: Adding: 2a = 11 → a = 5.5 (not integer) → No solution with integer digits Alternative approach: Try digit pairs where a+b=10 and a-b=1 → a=5.5, b=4.5 (invalid) So check other possibilities or different time gap.
Pro Tips & Tricks
- Any number minus its reverse is divisible by 9
- The difference between a number and its reverse = 9 × (difference of digits)
- Age reversal usually works for two-digit ages (10-99)
- The time gap must equal 9 × (digit difference)
- Possible digit differences: 1, 2, 3, 4 (giving time gaps 9, 18, 27, 36 years)
- The sum of digits often provides the second equation
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Reverse Age (Trick). Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Reverse Age (Trick) is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Reverse Age (Trick)?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: