What's the best way to master Ratio Chain quickly?

Master Ratio Chain by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Ratio Chain

Ratio Chain problems involve multiple age relationships expressed as ratios between different pairs of persons. These problems require connecting ratios into a single chain to find individual ages or a common multiplier.

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 Ratio Chain

Prerequisites

Ratio and proportion LCM concept Connecting multiple ratios

Why This Matters: Ratio Chain problems test your ability to work with multiple ratios simultaneously. They appear in 1-2 questions in mains level exams.

How to Solve Ratio Chain Problems

Step 1: Write all given ratios in the form A:B, B:C, C:D etc.

Step 2: Connect ratios by finding a common term between consecutive ratios

Step 3: Make the common term equal by using LCM of its values

Step 4: Write the combined ratio A:B:C:D in simplest form

Step 5: Use a common multiplier k to express actual ages

Step 6: Use any additional condition (sum, difference, etc.) to find k

Pro Strategy: Connect ratios through common terms. Always simplify the combined ratio to its lowest terms before applying the multiplier.

Example Problem

Example: A:B = 2:3, B:C = 4:5, and sum of their ages is 105 years. Find each age. Solution: Step 1: A:B = 2:3, B:C = 4:5 Step 2: Make B common: In first ratio B=3, in second B=4 → LCM of 3 and 4 = 12 Step 3: A:B = 2:3 = 8:12, B:C = 4:5 = 12:15 Step 4: Combined A:B:C = 8:12:15 Step 5: Let ages be 8k, 12k, 15k Step 6: Sum = 8k + 12k + 15k = 35k = 105 → k = 3 Step 7: Ages: A = 24, B = 36, C = 45 years Answer: A=24, B=36, C=45 years

Pro Tips & Tricks

Find the person who appears in two ratios to connect them
Use LCM to make common terms equal
Write ratios in the form A:B, B:C to connect easily
The combined ratio shows relative ages of all persons
Multiply each ratio term by the same factor to maintain proportion
Check if the combined ratio can be simplified further

Shortcut Methods to Solve Faster

Combined ratio = multiply across after making middle terms equal

For three persons: A:B and B:C → A:B:C = (A×LCM/B₁):LCM:(C×LCM/B₂)

Use cross-multiplication to verify ratio chains

Common Mistakes to Avoid

Not making the common term equal before combining

Using addition instead of LCM to combine ratios

Forgetting to apply the multiplier to all terms

Misaligning terms when writing combined ratio

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Ratio Chain. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.

Worksheet 1 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 2 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 3 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 4 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 5 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 6 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 7 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 8 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 9 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 10 Advanced Advanced level - Challenge yourself with complex problems