🗺️ Chapter Roadmap
1 Present, Past & Future
Age problems are essentially Algebra word problems. The secret to solving them is to pick a "Base Person" and set their Present Age as x.
Past
"5 years ago"
Present
"Today / Now"
Future
"After 5 years / Hence"
2 Forming the Equation
In competitive exams (NTS, GAT), questions are wordy. You must translate keywords into symbols:
| Keyword in Question | Algebraic Meaning |
|---|---|
| "Twice as old" / "Two times" | 2 × x |
| "5 years younger than..." | x − 5 |
| "The sum of their ages..." | x + y |
| "The difference of their ages..." | x − y |
3 Ratio-Based Problems
If the ages of A and B are in the ratio 3 : 4, do not just use 3 and 4. Use 3x and 4x as their actual ages. This allows you to create a solvable equation.
Example: "Ratio of A and B is 2 : 3. After 5 years, their ratio becomes 3 : 4."
Equation: 2x + 53x + 5 = 34
4 The Law of Age Difference
💡 The Golden Exam Hack
"The difference between the ages of two people NEVER changes."
If your brother is 3 years older than you today, he was 3 years older when you were born, and he will be 3 years older 50 years from now.
In Exams: If a question says the difference is 10 years and the ratio is 1:2, then x = 10, and their ages are 10 and 20 instantly!
📝 Multi-Step Solved Example:
Question: Ali is twice as old as Asad. 5 years ago, Ali was 3 times as old as Asad. Find Asad's present age.
Asad = x
Ali = 2x (Because he is twice as old)
Asad was: x − 5
Ali was: 2x − 5
(2x − 5) = 3 × (x − 5)
2x − 5 = 3x − 15
15 − 5 = 3x − 2x
10 = x