Two Clue Chain
Two Clue Chain problems present exactly two relationship statements about ages, such as 'A is twice as old as B' and 'Five years ago, A was three times as old as B'. These two clues are sufficient to determine the present ages.
What You'll Learn
Introduction to Two Clue Chain
Two Clue Chain problems present exactly two relationship statements about ages, such as 'A is twice as old as B' and 'Five years ago, A was three times as old as B'. These two clues are sufficient to determine the present ages.
Prerequisites
How to Solve Two Clue Chain Problems
Step 1: Let the present age of the first person be x and the second person be y (or use one variable for both if relationship is direct)
Step 2: Translate the first clue into a mathematical equation
Step 3: Translate the second clue by adjusting ages (subtract for past, add for future)
Step 4: Write both equations and solve using substitution or elimination
Step 5: Verify your solution by checking both original clues
Step 6: Answer the specific question asked (present age, future age, or past age)
Example Problem
Example: A is twice as old as B. Five years ago, A was three times as old as B. Find their present ages. Solution: Step 1: Let B's age = x, then A's age = 2x Step 2: Five years ago: (2x - 5) = 3(x - 5) Step 3: 2x - 5 = 3x - 15 → 2x - 3x = -15 + 5 → -x = -10 → x = 10 Step 4: B = 10 years, A = 20 years Step 5: Check: Five years ago, A=15, B=5 → 15 is 3 times 5 ✓ Answer: A is 20 years old, B is 10 years old
Pro Tips & Tricks
- Use a single variable when one age is expressed in terms of the other
- For 'n years ago', subtract n from both ages in the equation
- For 'n years later', add n to both ages in the equation
- Write equations exactly as the statement reads before simplifying
- Always check if ages are positive integers (reasonable age values)
- Cross-verify by plugging answers back into both clues
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Two Clue Chain. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Two Clue Chain is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Two Clue Chain?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: