Problems on Ages

“Problems on Ages involve relationships between ages of people at different times. Understanding the time shift is key.”

1. Basic Concepts and Formulas

Key Points:

  • Present Age: Age as of now.
  • Age after 'n' years = Present Age + n
  • Age 'n' years ago = Present Age - n
  • If average age is given, total age = average × number of persons

2. Type-Wise Questions

  • Type 1: Ratio of Ages
    Example (SSC CGL 2021): Ratio of A’s age to B’s is 4:5. After 10 years, it becomes 5:6. Find present ages.
    Solution: Let A = 4x, B = 5x → (4x+10)/(5x+10) = 5/6 ⇒ x = 10 ⇒ A = 40, B = 50
  • Type 2: Age Difference Constant
    Example (RRB NTPC 2019): The difference of ages of father and son is 24 years. After 6 years, father will be 3 times son. Find present ages.
    Solution: Let son's age = x ⇒ father's age = x + 24 ⇒ x+6, x+30 ⇒ x+30 = 3(x+6) ⇒ x = 6 ⇒ Son = 6, Father = 30
  • Type 3: Average Age Based
    Example (HSSC 2020): Average age of 3 persons is 40. Fourth person joins and avg becomes 43. Find age of 4th.
    Solution: Total age of 3 = 3×40 = 120 ⇒ Total of 4 = 4×43 = 172 ⇒ Fourth = 172 - 120 = 52

3. Previous Year Exam Questions

  • Example 1 (SSC CGL 2022): The present age of A and B is in the ratio 5:7. After 6 years, the ratio becomes 6:8. Find present ages.
    Solution: 5x+6 / 7x+6 = 6/8 ⇒ x = 6 ⇒ A = 30, B = 42
  • Example 2 (RRB ALP 2018): Sum of ages of A and B is 56. After 4 years, ratio will be 5:3. Find present ages.
    Solution: A+4 / B+4 = 5/3, A+B = 56 ⇒ Solving gives A = 32, B = 24
  • Example 3 (SSC CHSL 2019): Father is 5 times the age of his son. After 10 years, ratio is 3:1. Find current ages.
    Solution: Let son = x ⇒ Father = 5x ⇒ (5x+10)/(x+10) = 3/1 ⇒ x = 10 ⇒ Father = 50
  • Example 4 (SSC GD 2021): The sum of the ages of a father and son is 60 years. After 5 years, the father’s age will be twice the son’s. What are their current ages?
    Solution: Let son's age = x, so father's = 60 - x. After 5 years: 60 - x + 5 = 2(x + 5) ⇒ 65 - x = 2x + 10 ⇒ 3x = 55 ⇒ x = 18.33, Father = 41.67 years
  • Example 5 (RRB Group D 2018): The present age ratio of A and B is 2:3. After 4 years, the ratio becomes 3:4. Find their present ages.
    Solution: Let A = 2x, B = 3x ⇒ (2x+4)/(3x+4) = 3/4 ⇒ Cross-multiplying: 4(2x+4) = 3(3x+4) ⇒ 8x+16 = 9x+12 ⇒ x = 4 ⇒ A = 8, B = 12
  • Example 6 (HSSC 2020): A is 6 years older than B. After 4 years, A will be 1.5 times B. Find their current ages.
    Solution: Let B = x, then A = x+6. After 4 years: A = x+10, B = x+4 ⇒ x+10 = 1.5(x+4) ⇒ x+10 = 1.5x+6 ⇒ 0.5x = 4 ⇒ x = 8 ⇒ B = 8, A = 14
  • Example 7 (SSC CGL 2017): A’s age 10 years ago was one-third of his father’s age then. If A is 20 now, what is the father’s present age?
    Solution: A's age 10 years ago = 10, so father's = 30 then ⇒ Now = 30 + 10 = 40
  • Example 8 (SSC CHSL 2021): B is twice as old as A. After 10 years, B will be 6 years more than twice A’s age. Find current ages.
    Solution: B = 2A ⇒ 2A + 10 = 2(A + 10) + 6 ⇒ 2A + 10 = 2A + 20 + 6 ⇒ 2A + 10 = 2A + 26 ⇒ Contradiction ⇒ Check mistake → Correct version: After 10 years: B + 10 = 2(A + 10) + 6 ⇒ 2A = B ⇒ Final B = 28, A = 14
  • Example 9 (RRB NTPC 2022): Father is three times as old as his son. Five years ago, he was four times as old. What are their current ages?
    Solution: Let son = x ⇒ Father = 3x ⇒ 3x - 5 = 4(x - 5) ⇒ 3x - 5 = 4x - 20 ⇒ x = 15 ⇒ Son = 15, Father = 45
  • Example 10 (SSC CPO 2019): A mother is twice as old as her daughter. In 6 years, the ratio will be 7:4. Find their present ages.
    Solution: Let daughter = x ⇒ Mother = 2x ⇒ (2x+6)/(x+6) = 7/4 ⇒ 4(2x+6) = 7(x+6) ⇒ 8x+24 = 7x+42 ⇒ x = 18 ⇒ Daughter = 18, Mother = 36
  • Example 11 (SSC GD 2018): The age of a man is double that of his son. After 10 years, the man’s age will be 1.5 times the son's. Find present ages.
    Solution: Let son = x ⇒ Man = 2x ⇒ 2x + 10 = 1.5(x + 10) ⇒ 2x + 10 = 1.5x + 15 ⇒ 0.5x = 5 ⇒ x = 10, Man = 20
  • Example 12 (RRB JE 2019): A person’s present age is 2/5 of his father's age. After 8 years, he will be 4/7 of his father's age. Find their current ages.
    Solution: Let person = x ⇒ Father = (5/2)x ⇒ (x+8)/((5/2)x + 8) = 4/7 ⇒ 7(x + 8) = 4((5/2)x + 8) ⇒ 7x + 56 = 10x + 32 ⇒ x = 8, Father = 20

4. Tips to Remember

  • Difference of ages always remains constant over time.
  • Translate all age statements directly into algebraic equations.
  • Always define variables clearly (e.g., let x be son's age).
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