Sum & Ratio
Sum and Ratio problems provide both the sum of ages and ratio relationships between persons. These problems require using the ratio to divide the total sum into individual ages.
What You'll Learn
Introduction to Sum & Ratio
Sum and Ratio problems provide both the sum of ages and ratio relationships between persons. These problems require using the ratio to divide the total sum into individual ages.
Prerequisites
How to Solve Sum & Ratio Problems
Step 1: Write the ratio of ages in simplest form (a:b:c)
Step 2: Sum of ratio terms = a + b + c
Step 3: Value of one ratio part = Total sum ÷ Sum of ratio terms
Step 4: Multiply each ratio term by this value to get individual ages
Step 5: If sum is for past/future, adjust ages first
Step 6: Verify that individual ages add up to the given sum
Example Problem
Example: The ages of A, B, and C are in the ratio 3:4:5. The sum of their ages is 72 years. Find each age. Solution: Step 1: Ratio = 3:4:5, sum of ratios = 3 + 4 + 5 = 12 Step 2: Value of one part = 72 ÷ 12 = 6 years Step 3: A = 3 × 6 = 18 years, B = 4 × 6 = 24 years, C = 5 × 6 = 30 years Answer: A=18, B=24, C=30 years
Pro Tips & Tricks
- Age = (Ratio term / Sum of ratios) × Total sum
- When sum is given for a different time, adjust ages first
- If ages are in ratio a:b, then ages are ak and bk
- Sum of ages = k(a+b) → k = sum/(a+b)
- Check if the ratio is in simplest form before calculating
- For three or more persons, extend the same principle
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Sum & Ratio. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Sum & Ratio is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Sum & Ratio?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: