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.

10Worksheets
200+Practice Questions
AdvancedDifficulty
3-4 hoursHours to Master

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

Two-digit number representation Digit reversal concept Linear equations Number theory basics
Why This Matters: Reverse Age problems are less common but appear in advanced exams like CAT and olympiads. You can expect 0-1 questions in SSC CGL and 1-2 in CAT.

How to Solve Reverse Age (Trick) Problems

1

Step 1: Let the two-digit age be represented as 10a + b

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Step 2: The reversed age is 10b + a

3

Step 3: Set up equation based on time difference

4

Step 4: For 'n years ago, age was reverse': (10a+b) - n = 10b + a

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Step 5: Simplify: 9a - 9b = n → 9(a-b) = n

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Step 6: Since n is between 1-99, a-b must be such that 9(a-b) = n

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Step 7: Find possible (a,b) pairs and verify reasonableness

Pro Strategy: Represent two-digit ages as 10a+b. Use the fact that difference between a number and its reverse is a multiple of 9: (10a+b) - (10b+a) = 9(a-b).

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

If present age = 10a+b, past age = 10b+a
Time gap = 9(a-b)
Digit sum = a+b

Common Mistakes to Avoid

Writing reversed age as ba instead of 10b+a
Forgetting that age must be two-digit for reversal to make sense
Not checking if reversed age is less than present age (should be for past)
Assuming all digit pairs yield valid ages

Exam Importance

Reverse Age (Trick) is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
0-1 questions
BANKING PO
0-1 questions
RAILWAYS RRB
0-1 questions
CAT
1-2 questions
INSURANCE
0-1 questions

Ready to Master Reverse Age (Trick)?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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