Complex Ratio Chain
Complex Ratio Chain problems involve multiple ratios connecting three or more persons (e.g., A:B = 2:3, B:C = 4:5). These problems require combining ratios into a single chain to find individual ages.
What You'll Learn
Introduction to Complex Ratio Chain
Complex Ratio Chain problems involve multiple ratios connecting three or more persons (e.g., A:B = 2:3, B:C = 4:5). These problems require combining ratios into a single chain to find individual ages.
Prerequisites
How to Solve Complex Ratio Chain Problems
Step 1: Write all given ratios in the form A:B, B:C, C:D etc.
Step 2: Identify a common person appearing in two ratios
Step 3: Make the common person's value equal using LCM
Step 4: Write the combined ratio A:B:C:D in simplest form
Step 5: Let actual ages be combined ratio terms multiplied by k
Step 6: Use any additional condition (sum, difference, etc.) to find k
Step 7: Calculate individual ages
Example Problem
Example: A:B = 2:3, B:C = 4:5. Sum of ages of A, B, C is 105 years. Find each age. Solution: Step 1: A:B = 2:3, B:C = 4:5 Step 2: Common term is B. In first ratio B=3, in second B=4 Step 3: LCM of 3 and 4 = 12 Step 4: A:B = 2:3 = 8:12, B:C = 4:5 = 12:15 Step 5: Combined A:B:C = 8:12:15 Step 6: Let ages be 8k, 12k, 15k Step 7: Sum = 8k+12k+15k = 35k = 105 → k = 3 Step 8: A = 24, B = 36, C = 45 years Answer: A=24, B=36, C=45 years
Pro Tips & Tricks
- Find the common person in consecutive ratios
- Use LCM of the common term's values to make them equal
- Write ratios in the form A:B, B:C to connect easily
- The combined ratio shows relative ages of all persons
- Simplify the final ratio to its lowest terms
- Use multiplier k to convert ratio to actual ages
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Complex Ratio Chain. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Complex Ratio Chain is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Complex Ratio Chain?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: