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Father-Son

Father-Son problems are classic age puzzles involving a parent and child. These problems typically use the constant age difference between father and son, combined with ratio relationships at different times.

10Worksheets
200+Practice Questions
BeginnerDifficulty
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 Father-Son

Father-Son problems are classic age puzzles involving a parent and child. These problems typically use the constant age difference between father and son, combined with ratio relationships at different times.

Prerequisites

Constant difference concept Ratio and proportion Linear equations
Why This Matters: Father-Son problems are the most common type of age problems. You can expect 2-3 questions in SSC CGL and 2-3 in banking exams.

How to Solve Father-Son Problems

1

Step 1: Let father's present age = F, son's present age = S

2

Step 2: Use the constant difference: F - S = d (constant over time)

3

Step 3: Translate ratio statements into equations (e.g., F/S = a/b)

4

Step 4: For past/future, adjust both ages equally

5

Step 5: Solve the equations simultaneously

6

Step 6: Verify the father is older than son and ages are reasonable

Pro Strategy: Use the ratio method with a common multiplier. The difference between father and son's ages remains constant - this is the key to verification.

Example Problem

Example: The ratio of father's age to son's age is 5:2. After 5 years, the ratio becomes 3:1. Find their present ages. Solution: Step 1: Let father = 5x, son = 2x Step 2: After 5 years: (5x + 5)/(2x + 5) = 3/1 Step 3: 5x + 5 = 3(2x + 5) → 5x + 5 = 6x + 15 Step 4: 5x - 6x = 15 - 5 → -x = 10 → x = 10 Step 5: Father = 50 years, Son = 20 years Answer: Father is 50, son is 20 years old

Pro Tips & Tricks

  • Father's age is always greater than son's age
  • Age difference remains constant over time
  • Use x as common multiplier when ratios are given
  • For 'm years ago', subtract m from both ages
  • For 'after n years', add n to both ages
  • The ratio approaches 1:1 as time passes

Shortcut Methods to Solve Faster

If ratio a:b and after n years ratio c:d, then n(c-d) formula applies
Father's age = n(c-d) × a/(ad - bc) pattern exists
Difference method: (a-b)n/(bc-ad) can find multiplier

Common Mistakes to Avoid

Assuming ratio applies to difference directly
Forgetting to add/subtract years from both ages
Not checking if father is old enough to be father
Mixing up numerator and denominator in ratio equations

Exam Importance

Father-Son 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

Ready to Master Father-Son?

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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