Problems on Ages

The purpose of this chapter is to explore a commonly occurring category of problems in competitive examinations: Problems on Ages. As the name suggests, these questions deal with the ages of one or more individuals and pose challenges by creating connections between their ages at different points in time. A sound understanding of arithmetic operations and elementary algebra is crucial to tackle these problems efficiently.

Importance in SSC, RRB, and Banking Exams

Problems based on ages are a staple in numerous competitive examinations, such as the Staff Selection Commission (SSC), Railway Recruitment Board (RRB), and various Banking Exams. In SSC exams, age-based problems often test the candidates’ mathematical reasoning skills. The RRB exams frequently include these problems as components of broader word problems, while banking exams may combine age-related problems with additional elements of percentage and ratio problems.

Basic Principles

Problems on ages primarily employ linear equations and basic mathematical principles. Here are a few common types of relationships you may need to understand:

1. Age Difference: The difference in age between two individuals remains constant over time.
2. Age Ratio: The ratio of ages of two individuals varies over time.
3. Total Age: The total of the ages of multiple individuals changes over time.

Mathematical Concepts Involved

A firm grasp of the following mathematical concepts is necessary to solve age-based problems:

1. Linear Equations: Formulating and solving linear equations is the primary tool for solving age-based problems.
2. Ratio and Proportions: The concept of ratios and proportions often comes in handy in age-related problems.
3. Percentage: Age problems sometimes involve the application of percentages.

Problem Solving Techniques and Examples

Using Linear Equations

Let’s start with a straightforward problem: John is twice as old as his son. The sum of their ages is 36. Find their ages.

Here, if we denote John’s son’s age as x years, John’s age becomes 2x. The sum of their ages is 36. Thus, we can set up the equation as x + 2x = 36, which gives x = 12. Hence, John’s son is 12 years old, and John is 24 years old.

Using Ratios

Consider the following problem: The current age ratio of A and B is 4:3. After 5 years, the ratio becomes 5:4. Find their current ages.

In this case, let the current ages of A and B be 4x and 3x years, respectively. After 5 years, their ages will be 4x + 5 and 3x + 5. Given that the ratio of their ages after 5 years is 5:4, we can form the equation (4x + 5) / (3x + 5) = 5 / 4. Solving this equation gives x = 5. Hence, A’s current age is 20, and B’s current age is 15.

Using Percentages

Take this problem as an example: Anuj’s age after 15 years will be 150% of his age 5 years ago. What is Anuj’s present age?

If we let Anuj’s present age be x years, his age after 15 years will be x + 15, and his age five years ago was x – 5. According to the problem, we can set up the equation as x + 15 = 1.5 * (x – 5). Solving this equation gives x = 30. Hence, Anuj’s current age is 30 years.

Practice Problems

Try to solve the following problems to get some practice:

1. Ten years from now, Peter will be twice as old as he was three years ago. How old is Peter now?
2. The ratio of James and John’s ages is 4:5. If James is 24, how old is John?
3. Linda is now four times older than her daughter. Four years ago, she was seven times older than her daughter was at that time. How old are they now?

Summary

Problems on ages require a clear understanding of basic arithmetic and linear equations. These problems typically involve establishing a relationship between the ages of different individuals at different points in time. With a firm understanding of the concepts and ample practice, these problems become quite manageable, even under the pressure of a timed exam. It’s also important to understand the question fully before formulating equations to prevent any mistakes.