“Problems on Ages” is a popular topic in the quantitative aptitude section of exams like IBPS PO, SSC CGL, RRB NTPC, and others. These problems involve calculating current, past, or future ages based on given conditions. In this guide, you’ll learn key formulas, shortcut tricks, and see solved examples to enhance your preparation.
Key Concepts and Formulas
- Age after n years = Present Age + n
- Age n years ago = Present Age – n
- n times the age = n × Present Age
- If ratio of ages is A:B, actual ages can be A×x and B×x
Shortcut Tricks to Solve Age Problems
Trick 1: Use Ratios to Form Equations
If the ratio of ages is given, assume a common variable and build equations.
Trick 2: Eliminate Options
In multiple-choice questions, test options using conditions to find the correct answer quickly.
Trick 3: Understand Average-Based Age Problems
Use total age = average × number of people.
Solved Examples
Example 1: Basic Age Relation
Q: 3 years ago, father was 7 times the son’s age. Now he is 5 times his age. Find their current ages.
A: Let son = x → father = 5x
7(x – 3) = 5x – 3 → x = 9
✅ Son = 9, Father = 45
Example 2: Sum of Ages
Q: Sum of mother and daughter is 50. Five years ago, mother was 7 times daughter.
A: Daughter = x, Mother = 50 – x → 7(x–5) = 45–x → x = 10
✅ Daughter = 10, Mother = 40
Example 3: Option Elimination
Q: Father is 5x son. Five years ago, he was 10x son. Options: 45, 40, 48…
A: Try 45 → Son = 9 → 5 yrs ago: 40 = 10×4 ✔ Correct
Average Age Questions
Example:
Average age of A & B = 25. Replacing A with C makes average 24. Replacing B with C gives 26.
- A + B = 50
- C + B = 48
- A + C = 52
Solving gives: C = 25, A = 27, B = 23
Family-Based Age Problems
Example:
Father = 4x sum of children. After 6 years, father = 3x their total age.
- (4x + 6) = 3(x + 18) → x = 12
- ✅ Father = 48
Practice Questions
- A is twice B. In 4 years, their age sum is 44. Find A & B.
- Ratio of two friends = 4:5. After 6 years = 5:6. Find present ages.
- Man is 4x son’s age. In 5 years, 3x. Find current ages.
Tips to Master Problems on Ages
- Read carefully to identify current vs. past/future ages.
- Always simplify ratios and form equations.
- Use smart guessing and elimination where possible.
- Practice different patterns regularly.
Relevant Exams
These problems appear frequently in:
Mastering problems on ages is about understanding relationships and solving equations efficiently. Use shortcuts, practice smartly, and you’ll ace these questions in your next exam!
