01 Key Concepts
Present vs. Past/Future Age
If present age is x, age n years ago was (x - n), and age n years from now will be (x + n).
Setting Up Equations
Translate word relationships ('twice as old', 'sum of ages') directly into algebraic equations using a variable for one age.
Ratio of Ages
When ages are given as a ratio, represent them using a common multiplier (e.g., 3x and 5x).
Age Difference is Constant
The difference between two people's ages never changes over time, even though both ages increase.
02 Solved Examples
Example 1 A father is 3 times as old as his son. In 5 years, he will be 2.5 times as old. Find their present ages.
- Let son's age = x, father's age = 3x.
- In 5 years: 3x+5 = 2.5(x+5).
- 3x+5 = 2.5x+12.5.
- 0.5x = 7.5, so x = 15.
- Father's age = 3x = 45.
Answer: Son = 15, Father = 45
Example 2 The sum of a mother's and daughter's ages is 50. The mother is 20 years older. Find both ages.
- Let daughter = x, mother = x+20.
- x + (x+20) = 50.
- 2x = 30, x = 15.
- Mother = 15+20 = 35.
Answer: Daughter = 15, Mother = 35
Example 3 The ratio of two friends' ages is 4:5, and the older is 20. Find the younger's age.
- Let ages be 4x and 5x.
- 5x = 20, so x = 4.
- Younger age = 4x = 4x4.
Answer: 16
03 Practice Questions
1A is twice as old as B. Their ages sum to 30. Find both ages.
A=20, B=10
25 years ago, a person was 20. What is their age now?
25
3In 10 years, a person will be 40. What is their age now?
30
4Ages are in ratio 2:3, and the younger is 14. Find the older's age.
21
5A father is 25 years older than his son; the son is 10. Find the father's age.
35
📄 Age Problems — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.