Sum of Ages

Sum of Ages problems provide the total sum of ages of two or more persons. These problems often combine sum information with other relationships like ratios or differences to find individual ages.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

Introduction to Sum of Ages

Sum of Ages problems provide the total sum of ages of two or more persons. These problems often combine sum information with other relationships like ratios or differences to find individual ages.

Prerequisites

Basic arithmetic Linear equations with one variable Understanding of sum concept
Why This Matters: Sum of Ages problems appear in 2-3 questions in most competitive exams. They test basic equation formation skills.

How to Solve Sum of Ages Problems

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Step 1: Identify all persons whose ages are to be summed

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Step 2: Write the sum equation: Age1 + Age2 + ... = Total

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Step 3: Express each age in terms of a single variable if relationships exist

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Step 4: Substitute into the sum equation

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Step 5: Solve for the variable

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Step 6: Calculate individual ages

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Step 7: Verify that the sum matches the given total

Pro Strategy: Express all ages in terms of the youngest person's age to minimize variables. Use the sum equation to solve for the base variable.

Example Problem

Example: The sum of ages of A and B is 50 years. A is 10 years older than B. Find their ages. Solution: Step 1: Let B = x, then A = x + 10 Step 2: Sum: (x + 10) + x = 50 Step 3: 2x + 10 = 50 → 2x = 40 → x = 20 Step 4: B = 20, A = 30 years Answer: A = 30, B = 20 years

Pro Tips & Tricks

  • Sum = Age1 + Age2 + ...
  • If ages are in ratio a:b, then sum = k(a+b)
  • If one person is x years older, express the older as younger + x
  • For three or more persons, systematically reduce variables
  • The average age = Sum ÷ Number of persons
  • Future sum = Present sum + (n × number of persons)

Shortcut Methods to Solve Faster

If two persons with difference d, then younger = (Sum - d)/2
Older = (Sum + d)/2
For three in AP, middle age = Sum/3

Common Mistakes to Avoid

Forgetting to include all persons in the sum
Miscounting the number of persons
Using wrong operation when expressing relationships
Not verifying that individual ages add to given sum

Exam Importance

Sum of Ages is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Sum of Ages?

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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