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Multiple Generations

Introduction

Some age problems involve multiple generations such as a grandfather, father, and son. Instead of just comparing two people, the problem relates their ages across generations.

These questions look slightly more complex, but the approach is simple: represent each generation’s age using variables and known relations, then form equations step by step.

Pattern: Multiple Generations

Pattern

The key idea:

Express each generation’s age in terms of one variable (usually the youngest).

Use the relations given (like twice, thrice, or age differences after certain years) to form equations and solve them.

Step-by-Step Example

Question

A father is 3 times as old as his son. After 12 years, the father will be twice as old as the son. Find their present ages.

Options:

  • A: Father 36, Son 12
  • B: Father 40, Son 20
  • C: Father 30, Son 15
  • D: Father 45, Son 18

Solution

  1. Step 1: Represent ages with a variable.

    Let the son’s present age = x.
    Father’s present age = 3x.

  2. Step 2: Use the given condition.

    After 12 years, the father will be twice the son’s age.

    Father after 12 years = 3x + 12
    Son after 12 years = x + 12
    Condition → 3x + 12 = 2(x + 12)

  3. Step 3: Solve the equation.

    3x + 12 = 2x + 24
    x = 12

  4. Step 4: Find actual ages.

    Son = 12
    Father = 3 × 12 = 36

  5. Step 5: Final Answer:

    Father 36, Son 12 → Option A

  6. Step 6: Quick Check:

    After 12 years → Son = 24, Father = 48 → 48 = 2×24 ✅

Quick Variations

Sometimes, the relation is between grandfather, father, and son. In such cases, always express everyone's age in terms of the youngest person.

For example: If a grandfather is 4 times as old as his grandson, and 30 years older than the father, you can form equations in the same way.

Trick to Always Use

  • Step 1: Assign a variable to the youngest generation.
  • Step 2: Write other ages in terms of that variable.
  • Step 3: Translate each sentence of the problem into an equation carefully (Sentence → Math).
  • Step 4: Solve step by step and double-check with the condition.

Summary

Summary

  • Step 1: Assign variable to the youngest.
  • Step 2: Express others in terms of it.
  • Step 3: Form equations from the statements.
  • Step 4: Solve and verify.

Example to remember:
Father = 3×son; after 12 years father = 2×son → form 3x+12 = 2(x+12) and solve.

Practice

(1/5)
1. A father is 25 years older than his son. The grandfather is 25 years older than the father. If the son is 20 years old, what is the grandfather’s age?
easy
A. 65
B. 70
C. 75
D. 80

Solution

  1. Step 1: Father’s age.

    Son = 20 → Father = 20 + 25 = 45.

  2. Step 2: Grandfather’s age.

    Grandfather = 45 + 25 = 70.

  3. Final Answer:

    70 → Option B

  4. Quick Check:

    20, 45, 70 follow 25-year gaps ✅
Hint: Add the gaps stepwise: son + 25 + 25.
Common Mistakes: Forgetting to add both generation gaps.
2. A man is 30 years older than his son. The grandfather is 20 years older than the man. If the son is 25, what is the grandfather’s age?
easy
A. 70
B. 75
C. 80
D. 85

Solution

  1. Step 1: Father's age.

    Son = 25 → Father = 25 + 30 = 55.

  2. Step 2: Grandfather's age.

    Grandfather = 55 + 20 = 75.

  3. Final Answer:

    75 → Option B

  4. Quick Check:

    Son 25, Father 55, Grandfather 75 - differences match ✅
Hint: Add generation gaps in correct order: son → father → grandfather.
Common Mistakes: Adding the difference to the son instead of the father.
3. A father’s age is three times his son’s age. The grandfather is twice the father’s age. If the son is 12, how old is the grandfather?
medium
A. 66
B. 70
C. 72
D. 75

Solution

  1. Step 1: Father’s age.

    Son = 12 → Father = 3 × 12 = 36.

  2. Step 2: Grandfather’s age.

    Grandfather = 2 × 36 = 72.

  3. Final Answer:

    72 → Option C

  4. Quick Check:

    12 : 36 : 72 = 1 : 3 : 6 as expected ✅
Hint: Apply multipliers one step at a time.
Common Mistakes: Jumping from son to grandfather multiplier directly.
4. A man is 4 times the age of his son. The grandfather is 20 years older than the man. If the son is 15, find the grandfather’s age.
medium
A. 75
B. 80
C. 85
D. 90

Solution

  1. Step 1: Father’s age.

    Son = 15 → Father = 4 × 15 = 60.

  2. Step 2: Grandfather’s age.

    Grandfather = 60 + 20 = 80.

  3. Final Answer:

    80 → Option B

  4. Quick Check:

    15, 60, 80 satisfy all relations easily ✅
Hint: Multiply first, then add the fixed gap.
Common Mistakes: Adding the 20 years to the son instead of the father.
5. A son is 20 years younger than his father. The father is 25 years younger than the grandfather. If the son is 25, how old is the grandfather?
hard
A. 65
B. 70
C. 75
D. 80

Solution

  1. Step 1: Father’s age.

    Son = 25 → Father = 25 + 20 = 45.

  2. Step 2: Grandfather’s age.

    Grandfather = 45 + 25 = 70.

  3. Final Answer:

    70 → Option B

  4. Quick Check:

    25, 45, 70 preserve both differences correctly ✅
Hint: Add gaps one generation at a time.
Common Mistakes: Forgetting one of the generation gaps.

Mock Test

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