Problems on Ages
Problems on Ages
Age problems require setting up algebraic equations from conditions about present, past, and future ages. Questions involve ratios, sums, differences, and multiples of ages across different points in time.
Key Idea
Age difference is permanent. If A is 5 years older than B today, A was 5 years older than B 10 years ago too. This single fact unlocks most age problems.
Core Formulas
Age Difference
Age difference is constant — it remains the same regardless of the year
To compare ages at different points in time
Ratio Method
Present ages = ak and bk; use condition to find k
When ages are given as ratio
Past Age
Age n years ago = Present age − n
For questions about past ages
Future Age
Age n years later = Present age + n
For questions about future ages
Average Age
Sum of ages = Average × Count; if one new member joins, new sum = old sum + new age
For group age questions
Relevant Exams
2–4 questions in almost every competitive exam. Age problems appear in both arithmetic and word problem sections. Mastering ratio-based setup solves 80% of questions.