ReasoningAbility.com

Triple Relation

Triple Relation problems involve age relationships among three persons simultaneously. These problems require setting up and solving three equations or using clever substitution techniques to find individual ages.

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

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Triple Relation

Triple Relation problems involve age relationships among three persons simultaneously. These problems require setting up and solving three equations or using clever substitution techniques to find individual ages.

Prerequisites

Linear equations with multiple variables Substitution method Elimination method
Why This Matters: Triple Relation problems test your ability to handle multiple variables. They appear in 1-2 questions in mains level exams and olympiads.

How to Solve Triple Relation Problems

1

Step 1: Assign variables to the ages of the three persons (x, y, z)

2

Step 2: Translate each relationship statement into an equation

3

Step 3: Look for ways to express two variables in terms of the third

4

Step 4: Use substitution to reduce to a single equation

5

Step 5: Solve for the first variable, then find the others

6

Step 6: Verify all three conditions are satisfied

Pro Strategy: Express all ages in terms of the youngest person's age to minimize variables. Work systematically through each relationship.

Example Problem

Example: A is twice as old as B. B is three years older than C. The sum of their ages is 43 years. Find each age. Solution: Step 1: Let C = x, then B = x + 3, A = 2(x + 3) = 2x + 6 Step 2: Sum: (2x + 6) + (x + 3) + x = 43 Step 3: 4x + 9 = 43 → 4x = 34 → x = 8.5 Step 4: C = 8.5 years, B = 11.5 years, A = 23 years Answer: A = 23, B = 11.5, C = 8.5 years

Pro Tips & Tricks

  • Start with the person who has the most relationships mentioned
  • Express all ages in terms of the smallest variable
  • Use the sum equation to solve for the base variable
  • Draw a relationship diagram to visualize connections
  • Check if ages are reasonable (positive, logical order)
  • For fractional answers, verify if problem accepts decimals

Shortcut Methods to Solve Faster

If A is m times B, and B is n years more than C, then A = m(C + n)
Sum of three ages in arithmetic progression: middle age × 3 = total
Use average age to find total and work backwards

Common Mistakes to Avoid

Misordering the relationships when translating to equations
Forgetting to apply time changes (past/future) to all three persons
Algebraic errors in multi-step substitution
Not verifying all three conditions after solving

Exam Importance

Triple Relation is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions

Ready to Master Triple Relation?

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

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now