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Fraction Change Over Time

Fraction Change Over Time problems involve a fractional relationship between ages that changes over time (e.g., 'A is 1/2 of B now, but will be 2/3 of B after 5 years'). These require solving for present ages using both fraction conditions.

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 Fraction Change Over Time

Fraction Change Over Time problems involve a fractional relationship between ages that changes over time (e.g., 'A is 1/2 of B now, but will be 2/3 of B after 5 years'). These require solving for present ages using both fraction conditions.

Prerequisites

Fraction operations Ratio concepts Time-based equations
Why This Matters: Fraction Change Over Time problems appear in 1-2 questions in advanced exams. They test understanding of fraction evolution over time.

How to Solve Fraction Change Over Time Problems

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Step 1: Convert fraction statements to equations (e.g., A = (p/q)B)

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Step 2: Let one variable be expressed in terms of the other

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Step 3: Apply time adjustment (add/subtract years) to both ages

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Step 4: Set up the second fraction equation at the other time

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Step 5: Solve the resulting equation(s)

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Step 6: Calculate both ages and verify both fractions

Pro Strategy: Convert fractions to ratios using a common multiplier to avoid fractions. The k-method works well for these problems.

Example Problem

Example: A is currently 1/3 of B's age. After 10 years, A will be 1/2 of B's age. Find present ages. Solution: Step 1: A = (1/3)B Step 2: Let B = 3k, A = k Step 3: After 10 years: (k+10)/(3k+10) = 1/2 Step 4: 2(k+10) = 3k+10 → 2k+20 = 3k+10 → 20-10 = 3k-2k → 10 = k Step 5: A = 10, B = 30 years Answer: A=10, B=30 years

Pro Tips & Tricks

  • Fraction p/q means ratio p:q
  • Use k method: A = pk, B = qk
  • The fraction increases over time (younger person catches up)
  • The denominator - numerator represents the constant age difference
  • Check if fractions are proper (numerator < denominator for younger)
  • The fraction approaches 1 as time increases

Shortcut Methods to Solve Faster

If A/B = a/b now and = c/d after n years, then B = n(bc-ad)/(ac-bd)
The constant difference = B - A = (q-p)k
Fraction change = (c/d - a/b) per n years

Common Mistakes to Avoid

Misplacing numerator and denominator in fractions
Forgetting that both ages change over time
Not simplifying fractions before solving
Assuming fraction increases or decreases incorrectly

Exam Importance

Fraction Change Over Time 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
1-2 questions

Ready to Master Fraction Change Over Time?

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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