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Fractional Ratio

Fractional Ratio problems involve age relationships expressed as fractions (e.g., 'A is 2/3 of B's age' or 'C's age is 3/4 of D's age'). These problems require careful handling of fractions to avoid calculation errors.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 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 Fractional Ratio

Fractional Ratio problems involve age relationships expressed as fractions (e.g., 'A is 2/3 of B's age' or 'C's age is 3/4 of D's age'). These problems require careful handling of fractions to avoid calculation errors.

Prerequisites

Fraction operations Ratio concepts Linear equations with fractions
Why This Matters: Fractional Ratio problems appear in 1-2 questions in competitive exams. They test comfort with fractional relationships.

How to Solve Fractional Ratio Problems

1

Step 1: Convert fractional statements into equations (e.g., A = (p/q) × B)

2

Step 2: Clear fractions by multiplying both sides by the denominator

3

Step 3: Express all ages in terms of one variable using integer relationships

4

Step 4: Use additional conditions (sum, difference) to solve

5

Step 5: Calculate individual ages

6

Step 6: Verify the fractional relationships hold

Pro Strategy: Clear fractions by using a common multiplier. Express ages as multiples of a common variable to avoid fractional calculations.

Example Problem

Example: A is 3/4 of B's age. The sum of their ages is 56 years. Find their ages. Solution: Step 1: A = (3/4)B Step 2: Multiply by 4: 4A = 3B Step 3: Let B = 4k, then A = 3k Step 4: Sum: 3k + 4k = 7k = 56 → k = 8 Step 5: A = 24, B = 32 years Answer: A = 24, B = 32 years

Pro Tips & Tricks

  • A = (p/q)B → A:B = p:q (simplified)
  • Use a common multiplier k: A = pk, B = qk
  • Always simplify fractions to lowest terms first
  • Convert mixed fractions to improper fractions
  • For compound fractions, work step by step
  • Check if the fraction is of present age or future/past age

Shortcut Methods to Solve Faster

Fraction p/q → ratio p:q after clearing
Use k method: multiply each ratio term by k
For A = p/q of B, difference = B - A = B(1 - p/q)

Common Mistakes to Avoid

Not clearing fractions before solving
Misinterpreting 'A is p/q of B' vs 'A is p/q more than B'
Forgetting to simplify fractions
Using fraction values incorrectly in equations

Exam Importance

Fractional Ratio 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 Fractional Ratio?

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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