Cheatsheet: Problem on Ages | Cheatsheets for Bank Exams PDF Download

Introduction

Problems on ages are common in competitive exams like bank exams. These problems typically involve the ages of individuals at different points in time, and they require you to set up equations based on relationships between their ages. Solving these problems involves using basic algebraic principles to find the unknown ages or the relationship between different people's ages.

This cheatsheet provides the key concepts, formulas, tips, and solved examples to help you solve problems on ages quickly.

Theory

Basic Concept of Problems on Ages:

• In these problems, you are usually given the age of a person at present, past, or future and are asked to find their age at another time.

• Often, the problem involves a relationship between the ages of two or more people, such as "A's age is twice B's age" or "The sum of their ages is a certain value."

General Approach:

1. Read the Problem Carefully: Understand what is being asked. Identify key information like the present age, the difference between ages, and the time periods involved.

2. Translate the Information into Equations: Let the unknown ages be represented by variables. Use the relationships given in the problem to form an equation.

3. Solve the Equation: Use algebra to solve the equation and find the required ages.

4. Verify the Solution: Check if the solution satisfies all the conditions given in the problem.

Important Formulas

1. Let the Present Age be x:

   • If the present age of a person is x, their age after n years will be (x + n).

   • Their age n years ago will be (x - n).

2. Relation Between Two Ages:

   • Example 1: If "A's age is twice B's age," then:

     • A = 2B

   • Example 2: If "A is 5 years older than B," then:

     • A = B + 5

3. Age Difference:

   • If the difference between the ages of two people is constant, it will not change with time.

   • Example: If A is 10 years older than B, the age difference is A - B = 10 and will remain the same even after a certain number of years.

4. Sum of Ages:

   • If the sum of the ages of two people is given, say A + B = 40, use it to form an equation.

5. A’s Age n Years Ago:

   • If A's present age is x and it is given that n years ago A's age was y, then:

     • x - n = y

     • Solving this gives A’s present age x = y + n.

Tips for Solving Problems on Ages Quickly

1. Define Variables for Unknowns:

• Always start by defining the present ages of the individuals as variables (x, y, etc.). This will make it easier to set up equations.

2. Use Relationships Between Ages:

• Often, the problem provides a relationship between the ages (e.g., "A is twice as old as B"). Use this to form an equation.

3. Use the Past and Future Relationships:

• If the problem mentions a change in age over time (e.g., "In 5 years, A will be 25"), express the future or past age in terms of the present age.

4. Be Careful with Age Differences:

• The age difference remains constant. For example, if A is 5 years older than B, this difference will not change with time.

5. Check Your Solution:

• After solving the equation, plug your values back into the original relationships to verify that they hold true.

Conclusion

Problems on ages in bank exams are straightforward once you identify the relationships between the ages and translate them into algebraic equations. Follow the steps:

1. Define the present ages.

2. Use the relationships to form equations.

3. Solve the equations carefully.

By practicing these problems regularly and applying the formulas and tips mentioned, you can solve them quickly and accurately during your bank exams.