Multi-Stage Age (Phased)
Multi-Stage Age Phased problems involve conditions at multiple points in time (e.g., '3 years ago, A was twice B; after 5 years, A will be 1.5 times B'). These problems require setting up multiple equations from different time points.
What You'll Learn
Introduction to Multi-Stage Age (Phased)
Multi-Stage Age Phased problems involve conditions at multiple points in time (e.g., '3 years ago, A was twice B; after 5 years, A will be 1.5 times B'). These problems require setting up multiple equations from different time points.
Prerequisites
How to Solve Multi-Stage Age (Phased) Problems
Step 1: Let present ages be variables (e.g., A = x, B = y)
Step 2: Translate each time-based condition into an equation
Step 3: For 'n years ago', use (x-n) and (y-n)
Step 4: For 'after n years', use (x+n) and (y+n)
Step 5: Write all equations from the given conditions
Step 6: Solve the system of equations using substitution or elimination
Step 7: Verify all conditions at all time points
Example Problem
Example: 5 years ago, A was 3 times as old as B. After 10 years, A will be 2 times as old as B. Find present ages. Solution: Step 1: Let A = x, B = y Step 2: 5 years ago: (x-5) = 3(y-5) → x - 5 = 3y - 15 → x - 3y = -10 ...(1) Step 3: After 10 years: (x+10) = 2(y+10) → x + 10 = 2y + 20 → x - 2y = 10 ...(2) Step 4: Subtract (1) from (2): (x-2y) - (x-3y) = 10 - (-10) → y = 20 Step 5: From (2): x = 10 + 2×20 = 50 Answer: A = 50, B = 20 years
Pro Tips & Tricks
- Draw a timeline marking all given time points
- Each time condition gives one equation
- Two conditions usually give two equations solvable for two variables
- The age difference remains constant across all time points
- Use the difference between equations to eliminate variables efficiently
- Check that all past ages are positive
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Multi-Stage Age (Phased). Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Multi-Stage Age (Phased) is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Multi-Stage Age (Phased)?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: