Age Problems - Examples and Questions with Answers

algebra Jun 03, 2021

What are Age Problems?

Age problems are algebra word problems that deal with people’s ages at different times, namely past, present and future. It can involve one single person or multiple people. Here’s an example to show you:

Example:
Pam is 20 years older than Mark. In 3 years, Pam will be three times as old as Mark. How old is Pam now?

Age Word Problems based on Present Ages

These type of age problems focus on finding the present age of one or more person(s) or thing(s).

Questions:

  1. Jacob is Sam’s father. Jacob is 40 years old. Two years ago, Jacob was two times as old as Sam was then. How old is Sam now?
  2. Erica is 10 years younger than Mike. If the sum of their ages is 36. How old is Erica?
  3. Paul is four times as old as Ryan. Paul is also six years older than Ryan. How old is Ryan?
  4. Eva is four times as old as Maria today. Six years ago, Eva was six times as old as Maria. How old is Eva now?
  5. Kayle’s father is five times older than Kayle and Kayle is twice as old as his brother Kevin. In two years time, the sum of all their ages will be 58 years. How old is Kayle now?

 Answers:

  1. 21 years
  2. 13 years
  3. 2 years
  4. 60 years
  5. 8 years

Age Word Problems based on Past Ages

These type of age problems focus on finding the age of one or more person(s) or thing(s) at a given point in the past.

Questions:

  1. Jessica is 5 years more than four times Eve’s age. 5 years ago, Jessica was five times as old as Eve. How old was Eve 3 years ago?
  2. Marie is twice as old as Jim. The sum of their ages seven years ago was 13. How old were they three years ago?
  3. Henry is six years older than Sally. Two years ago, Henry was three times as old as Sally. How old was Sally two years ago?
  4. The sum of the ages of Oliver and Gilbert is three times Gilbert’s age. Seven years ago, Oliver was three less than four times as old as Gilbert. How old were they two years ago?
  5. Colby is twice as old as Sienna and Richard is 9 years older than Sienna. 3 years ago, Colby was 9 years less than 3 times Sienna’s age. How old was Richard five years ago?

Answers:

  1. 22 years
  2. Marie: 15 years old; Jim: 6 years old
  3. 8 years
  4. Oliver: 22 years old; Gilbert: 10 years old
  5. 10 years

Age Word Problems based on Future Ages

These type of age problems focus on finding the age of one or more person(s) or thing(s) at a given point in the future.

Questions:

  1. A Chair is 4 years old and a Table is 10 years old. In how many years will the table be twice as old as the chair?
  2. Lily is 5 years older than John. Six years from now, the sum of their ages will be 79. Find the present age of Lily?
  3. Mr Wilson is 45 years old. His son is 20 years younger than him. In how many years will Mr Wilson’s age be 36 years less than three times as old as his son?
  4. Martha is twice as old as his friend Kim. Kim is 5 years older than Stuart. In 5 years, Martha will be three times as old as Stuart. How old is Kim two years from now?
  5. The sum of the ages of Ross and his Son is 38 years. Ross will be triple his son’s age in 9 years. How old will be Ross in two years?

Answers:

  1. 2 years
  2. 36 years
  3. 3 years
  4. 7 years
  5. 35 years

How to solve Age Problems?

Example 1: Kayle’s father is five times older than Kayle and Kayle is twice as old as his brother Kevin. In two years time, the sum of all their ages will be 58 years. How old is Kayle now?

Solution:


 

Example 2: Colby is twice as old as Sienna and Richard is 9 years older than Sienna. 3 years ago, Colby was 9 years less than 3 times Sienna’s age. How old was Richard five years ago? 

Solution:


 

Example 3: The sum of the ages of Ross and his Son is 38 years. Ross will be triple his son’s age in 9 years. How old will be Ross in two years?

Solution:

To learn more about 11+ Advanced Algebra topics, word problems and how to solve them, view our video lessons on Advanced Algebra Word Problems for 11+ Exams.

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