Hidden Equation
Hidden Equation problems present age relationships in non-standard or indirect ways. You must identify the mathematical equation hidden within the wording before solving.
What You'll Learn
Introduction to Hidden Equation
Hidden Equation problems present age relationships in non-standard or indirect ways. You must identify the mathematical equation hidden within the wording before solving.
Prerequisites
How to Solve Hidden Equation Problems
Step 1: Read the problem carefully multiple times
Step 2: Identify all numerical quantities mentioned
Step 3: Identify all relationships (comparisons, operations)
Step 4: Translate word statements into mathematical equations
Step 5: Look for hidden implications (e.g., 'as old as' means equal)
Step 6: Combine equations and solve
Step 7: Verify the solution against the original wording
Example Problem
Example: Ten years from now, A will be twice as old as B was ten years ago. If A is 10 years older than B, find their ages. Solution: Step 1: Let A = x, B = y Step 2: Ten years from now: A+10 Step 3: Ten years ago: B-10 Step 4: Condition: (x+10) = 2(y-10) Step 5: Given: x = y + 10 Step 6: Substitute: (y+10+10) = 2(y-10) → y+20 = 2y-20 → 40 = y → y=40, x=50 Answer: A = 50, B = 40 years
Pro Tips & Tricks
- 'As old as' means equal (=)
- 'Twice as old' means multiply by 2
- 'n years from now' means add n
- 'n years ago' means subtract n
- 'The age when' indicates a specific time point
- Draw a timeline for complex temporal references
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Hidden Equation. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Hidden Equation is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Hidden Equation?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: