How to Solve Age Word Problems
This post will teach how to solve age word problems in mathematics, as it is one of the important topic for job tests. It usually come in every job test. Therefore, students must explore some ideas and trick to solve the age word problem through this post. Lets begin.
Rules for Solving the Age Word Problems
Following are the rules to solve the age word problems. Students must remember these rule in order crack the age word problems:
- If your current age is x, multiply it by n to get nx.
- If your current age is x, your age n years later will be x + n.
- If your current age is x, your age n years ago is equal to x – n. The ages in a ratio of a:b are ax and bx.
- If the current age is x, then 1/n of the age is x/n
Examples on Ages Problems
Problem No. 1: Father is three years older than his son Jack. He’d be two and a half times Jack’s age in 8 years. How many times would he be Jack’s age after another 8 years?
Let Jack’s present age be x years.
Then, father’s present age =(x + 3x) years => 4x years.
(4x + 8) = 5 /2 (x + 8) => (after cross multiplication) => 8x + 16 = 5x + 40
8x-5x = 40-16 => 3x = 24 => x = 8.
Hence, required ratio = (4x + 16)/(x + 16) => 48/ 24 => 2
Problem No. 2: The total of the ages of five children born at three-year intervals is 50 years. What is the youngest child’s age?
Let the ages of five children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
x+x+3+x+6+x+9+x+12 = 50 => 5x = 50-30 => 5x = 20
5x = 20 => x = 20/5
x = 4.
Problem No. 3: “I was as old as you are now when you were born,” a father told his son. If the father is 38 years old now, the son was 5 years ago.
Let the son’s present age be x years.
Then, (38 – x) = x => x= 19.
Son’s age 5 years back = (19 – 5) = 14 years
Problem No. 4: Nikki and John’s ages were two and three years apart a year ago. After five years, this ratio will be 4: 5. John’s, how old are you now?
We are given that age ratio of Nikki: John= 2: 3
Nikki’s age = 2x and John’s age = 3x
One year ago, their age was 2x and 3x.
Hence at present, Nikki’s age = 2x +1 and John’s age = 3x +1
After 5 years, Nikki’s age = (2x +1) + 5 => (2x + 6)
John’s age = (3x +1) + 5 = (3x + 6)
After 5 years, this ratio becomes 4: 5.
Therefore, (2x+6) / (3x+6) = 4/5 10x + 30 = 12x + 24 ⇒ x = 3
John’s present age = (3x + 1) = (3x 3 + 1) = 10 years
Nikki’s present age = (2x + 1) = (2x 3 + 1) = 7 years