What's the best way to master Parent Child Multiple Age Problems quickly?

Master Parent Child Multiple Age Problems by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Parent-Child Multiple

Parent-Child Multiple problems involve age relationships between a parent and child, often stating that at some point in time, the parent's age is a multiple of the child's age. These classic problems test constant age difference and changing multiples over time.

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 Parent-Child Multiple

Prerequisites

Constant age difference concept Linear equations Understanding of 'n years ago' and 'after n years'

Why This Matters: Parent-Child Multiple problems are among the most common age problems. You can expect 2-3 questions in SSC CGL and 2-3 in banking exams.

How to Solve Parent-Child Multiple Problems

Step 1: Let the child's present age = x

Step 2: Express parent's present age in terms of x using given relationship

Step 3: Adjust both ages for the given time point (add for future, subtract for past)

Step 4: Set up the multiple equation at that time point

Step 5: Solve for x

Step 6: Calculate both ages

Step 7: Verify that the parent is old enough to be a parent (usually 20+ years older)

Pro Strategy: Always assign the variable to the younger person (child) to avoid fractions. Remember that the age difference remains constant while the multiple decreases over time.

Example Problem

Example: A father is 3 times as old as his son. 5 years ago, he was 4 times as old as his son. Find their present ages. Solution: Step 1: Let son = x, father = 3x Step 2: 5 years ago: father = 3x - 5, son = x - 5 Step 3: (3x - 5) = 4(x - 5) Step 4: 3x - 5 = 4x - 20 → 3x - 4x = -20 + 5 → -x = -15 → x = 15 Step 5: Son = 15, Father = 45 years Answer: Father = 45, Son = 15 years

Pro Tips & Tricks

Let child's age = x to avoid fractions
Parent's age = m × child's age (where m > 1)
Age difference = Parent - Child = (m-1)x
After n years, multiple decreases (approaches 1)
n years ago, multiple was larger
Check biological plausibility: parent should be at least 18-20 years older

Shortcut Methods to Solve Faster

If ratio a:b now and c:d after n years, use formula for x

x = n(c-d)/(ad-bc) for two persons

Parent's age = m × Child's age always

Common Mistakes to Avoid

Assigning variable to parent creates fractions

Forgetting to apply time change to both persons

Not checking if parent is old enough (minimum age difference 18 years)

Using wrong multiplier (using 1/3 instead of 3)

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Parent-Child Multiple. 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