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Double/Half

Double-Half problems involve relationships where one person's age is double (or half) of another's age, either at present or at some time in the past/future. These are fundamental age relationship problems.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 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 Double/Half

Double-Half problems involve relationships where one person's age is double (or half) of another's age, either at present or at some time in the past/future. These are fundamental age relationship problems.

Prerequisites

Basic algebra Understanding of multiples Linear equations
Why This Matters: Double-Half problems appear in 2-3 questions in most competitive exams. They form the core of age problem solving.

How to Solve Double/Half Problems

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Step 1: Let the smaller age = x, larger age = 2x (or vice versa)

2

Step 2: Apply time adjustments (past/future) to both ages

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Step 3: Set up equation based on the condition at that time

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Step 4: Solve for x

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Step 5: Calculate both ages

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Step 6: Verify the relationship holds

Pro Strategy: Always assign the variable to the younger person when dealing with 'double' relationships to avoid fractions.

Example Problem

Example: A is twice as old as B. 10 years ago, A was four times as old as B. Find present ages. Solution: Step 1: Let B = x, A = 2x Step 2: 10 years ago: (2x - 10) = 4(x - 10) Step 3: 2x - 10 = 4x - 40 → -10 + 40 = 4x - 2x → 30 = 2x → x = 15 Step 4: B = 15, A = 30 years Answer: A = 30, B = 15 years

Pro Tips & Tricks

  • Let the smaller age be x to avoid fractions
  • For 'half of', let larger = x, smaller = x/2 (or use 2x and x)
  • Double means multiply by 2, half means divide by 2
  • The ratio of ages changes over time (approaches 1:1)
  • The age difference remains constant even when ratio changes
  • Check if the older person is realistically older

Shortcut Methods to Solve Faster

If A = 2B now, and A = kB n years ago, then B = n(k-2)/(2-k)
Difference method: (2-1) × B = difference = constant
For half problems, multiply both sides to avoid fractions

Common Mistakes to Avoid

Assigning variable to the older person creates fractions
Forgetting that both ages change over time
Using wrong multiplier (using 1/2 instead of 2)
Not checking if past ages are possible (positive)

Exam Importance

Double/Half is an important topic for various competitive exams. Here's how frequently it appears:

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

Ready to Master Double/Half?

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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