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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
2.8 Word Problems - Age

1. Read the problem carefully and note down what is given and what is required.
2. Select a letter say x or y or z to represent the unknown quantity asked for.
3. Represent the word statements of the problems in the symbolic language step by step.
4. Look for quantities which are equal as per conditions given and form an equation.
5. Solve the equation.
6. Verify the result for making sure that your answer satisfies the requirements of the problems.

Five years ago the age of a father was twice the age of his son. The sum of their present ages is 55 years. Find their present ages.
The age of the father, 5 years ago = x years
Age of the father 5 years ago = 2x years
Present ages of son and father respectively are (x+5) years and (2x+5)years.
Given that, sum of their present ages = 55 years
Therefore (x+5)+(2x+5) = 55
3x + 10 = 55
3x = 55 - 45
3x = 45
x = 45/3
x = 15

Present age of son = x + 5 = 15 + 5 = 20 years
Present age of father = 2x + 5 = 2*15 + 5 = 30 + 5 = 35 years
The sum of their present ages = 20 + 35 = 55 years.

Directions: Solve the following word problems. Also write at least ten word problem examples of your own.
Q 1: The present age of Adam is three times that of his son. Six years ago, the age of Adam was four times that of his son. Find the ratio of their ages 6 years later.

Q 2: Present ages of Ron and Matt are 20 and 5 years respectively. After how many years will the age of Ron be twice that of Matt.
12 years
16 years
14 years
10 years

Q 3: George aged 50 years, has a daughter Jessica of age 20 years. How many years ago was the age of George three times that of his daughter.

Q 4: John is 35 years old and his son 7 years now. In how many years will the son be half as old as his father. (Hint equation: 7 + x = 1/2(35 + x) )

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!

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