Problems on Ages

Overview

Problems on Ages form a consistent 1–2 question segment in IBPS PO Prelims, appearing either as standalone questions or embedded within data interpretation sets. These problems test your ability to translate verbal age relationships into algebraic equations and solve them efficiently.

The good news: age problems rely on a single, unchanging principle—**everyone ages at the same rate**. If 5 years pass, every person in the problem becomes exactly 5 years older. Master this concept, set up clean equations, and these become free marks. Most questions involve linear equations in one or two variables, occasionally combined with ratio manipulation.

This topic also builds foundational skills for partnership, time-work, and other ratio-based problems. Investing time here pays dividends across the Quantitative Aptitude section.

Key Concepts

• **Universal aging rule**: If the present age is x, then age after t years = x + t, and age before t years = x − t. This applies uniformly to all persons.

• **Age difference is constant**: The gap between two people's ages never changes. If A is 10 years older than B today, A will always be 10 years older than B.

• **Ratio of ages changes over time**: While the difference stays constant, the ratio shifts. A ratio of 3:2 today won't remain 3:2 after 10 years.

• **Sum of ages changes predictably**: If there are n persons and t years pass, the total of their ages increases by n × t.

• **"Times as old" means multiplication**: "A is twice as old as B" translates to A = 2B, not A = B + 2.

• **Birth year problems**: When a person's birth year is asked, use Present Year − Present Age = Birth Year.

• **Negative age check**: Always verify your answer makes sense—ages cannot be negative or unrealistically large.

Formulas / Key Facts

| Scenario | Equation Setup | |----------|----------------| | Present ages in ratio a:b | Let ages = ax and bx | | A is n years older than B | A = B + n | | A is n times as old as B | A = n × B | | t years ago, ratio was m:n | (A − t)/(B − t) = m/n | | t years hence, ratio will be m:n | (A + t)/(B + t) = m/n | | Sum of ages = S | A + B + C + ... = S | | Product of ages = P | A × B = P |

**Quick calculation tip**: When present ratio is a:b and future/past ratio is c:d, the difference in ratio terms often helps find the multiplier directly.

Worked Examples

### Example 1: Basic Ratio Problem **Question**: The present ages of A and B are in the ratio 5:3. After 6 years, their ages will be in the ratio 7:5. Find A's present age.