# Problems on Ages — Timeline Method and Shortcuts

Source: https://skills101.in/learn/aptitude/problems-on-ages — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

Age problems look like riddles but they all use one fact:

> **Everyone gets older by the same amount. So the difference between two people's ages never changes.**

![Timeline: 5 years ago, now, after 5 years. Ravi's age is x−5, x, x+5 and his father's y−5, y, y+5](https://skills101.in/learn-img/aptitude/age-timeline.svg)

## The method

1. Choose **one** person's present age as x (or use a ratio like 3k and 5k).
2. Write every other age in terms of x, moving along the timeline (past: subtract, future: add — **for both people**).
3. Make one equation from the condition and solve.
4. **Check** your answer against the original sentence.

### Example 1
*A father is 30 years older than his son. In 5 years, the father will be 3 times as old as the son. Find their present ages.*

Son = x, father = x + 30. In 5 years: x + 35 = 3(x + 5) → x + 35 = 3x + 15 → x = 10.

Son = **10**, father = **40**. Check: in 5 years 15 and 45, and 45 = 3 × 15 ✓

### Example 2 — ratios
*The ratio of the ages of A and B is 4 : 5. Six years later it will be 5 : 6. Find their present ages.*

A = 4k, B = 5k. (4k + 6)/(5k + 6) = 5/6 → 24k + 36 = 25k + 30 → k = 6.

A = **24**, B = **30**.

> **Shortcut for ratios:** the difference stays the same. Now the difference is 1 part (5 − 4); later it is also 1 part (6 − 5). So "1 part" is the same number of years in both ratios. A goes from 4 parts to 5 parts in 6 years → 1 part = 6 → A = 24, B = 30.

### Example 3 — the past
*Ten years ago, Meera's age was half of what it will be 15 years from now. What is her present age?*

x − 10 = ½(x + 15) → 2x − 20 = x + 15 → x = **35**.

### Example 4 — sum of ages
*The sum of the ages of a mother and daughter is 50. Five years ago the mother was 7 times as old as the daughter. Find their ages.*

Daughter = x, mother = 50 − x. Five years ago: (45 − x) = 7(x − 5) → 45 − x = 7x − 35 → 8x = 80 → x = 10.

Daughter = **10**, mother = **40**.

### Example 5 — average of a family
*The average age of a husband and wife was 25 when they married. Six years later they have a child. The average age of the three is now 22. How old is the child?*

At marriage the couple's total was 2 × 25 = 50. Six years later it is 50 + 6 + 6 = 62. The family's total now is 3 × 22 = 66. Child = 66 − 62 = **4 years**.

## Use the options (a huge time-saver)

In an exam, you can plug each option into the question. Example 1 options might be (10, 40), (12, 42), (15, 45), (8, 38). Only (10, 40) passes "in 5 years father = 3 × son". This takes 20 seconds.

## Common mistakes

- Adding years to **one** person only. Time passes for everyone.
- Forgetting that the **difference** between ages stays the same — a free equation.
- Answering with the age at a different time (the question asks "present age" but you give the age "5 years later").

## Quick recap

- One variable + timeline.
- Age difference never changes.
- Ratios: use parts; the difference in parts is the same number of years.
- Plug in the options to check fast.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/problems-on-ages