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# Problem On Ages Questions and Answers

# Problem On Ages Questions

## Definition of Problem On Ages

**Problems on ages are a type of word problem based on algebra, which deals with the current, past, and future age of people. It can be further categorized into three forms, i.e. Questions for determining the present age, Questions for calculating the age of person after particular years, and questions that calculate the age of a person before given years. Moreover, these types of questions cover cases of different types with various combinations of ratios and fractions.**

**Important Statements and Equations: **

- If the present age is given as p, then q times the present age = ‘qp’
- If the present age is given as p, then age q years later/hence = p + q
- If the present age is given as p, then age q years ago = p – q.
- The age is given in the ratio p: q, then the age will be px and qx.
- If the present age is given as p, then 1/qth of the age is p/q.

**Common Expressions**

Below given are some of the frequent expressions that should be remembered while solving the problems on ages. In all the given expression, we assume x as the present age of a man.
- Man’s age five years hence or from now = (x + 5)
- Man’s age six years ago = (x – 6)
- The woman is four times as old as man= (Woman’s age : 4x)
- The woman is thrice as old as man five years ago = (Woman’s age : 3(x-5))

**Rules**

- It is essential to categorize the key expressions and arrange the information by assigning different variables to various unknown quantities in order to acquire the correct answer.
- Translate the given problem into algebraic equations with the help of variables and phrases which represent the problems.
- Select only one variable to solve the problem.
- Use methods such as elimination and matrix to solve the equations.
- If the information in the question comprises ages at different points of time, assume the present age as ‘x.’
- If the information in the question comprises ages of different people, assume the age of the youngest person as ‘x.’
- Read the question very carefully. The phrase ‘n time more than,’ ‘after x years,’ and ‘before x years’ needs to be understood correctly.
- Check the obtained answer, both mathematically and intuitively.