In the previous chapter, we covered Average and explored its important concepts and different types of questions, including questions involving ages. In this chapter, we will cover Age Problems in detail, learn the important concepts, formulas and methods, solve different types of questions, practice them, and finally work through previous-year questions (PYQs).
From a competitive-exam point of view, Age Problems are an important topic and require a clear understanding of concepts and regular practice. Questions from this topic are commonly asked in SSC, RRB, Banking, Defence, Police and other competitive examinations.
So, let us begin our preparation with Age Problems.
For complete and free competitive-exam Maths preparation, visit our Competitive Exams Maths section, where you can explore all the chapters in one place. To strengthen your concepts, visit our Maths Notes section; for formulas and quick revision, explore our Formula section; for chapter-wise practice, visit our Practice section; and for previous-year questions, explore our PYQs section.
Want to explore the complete competitive-exam Maths syllabus? Visit our dedicated Competitive Exams Maths Syllabus section.
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What are Age Problems?
Age Problems are mathematical questions in which the ages of two or more people are related through statements about their present, past, or future ages. You may be required to find the age of one person when the age of another person and their age relationship are given.
For example 1,
Aspirant A is 2 years younger than Aspirant B. If Aspirant B is 28 years old, what is the age of Aspirant A?
Solution:
Age of A = 28 − 2 = 26 years
Answer: 26 years
Age Problems Formula & Concepts
You can solve Age Problems easily by reading the question carefully, identifying the age relationships given, converting those relationships into mathematical equations, and then solving the equations.
For example 2:
The age of A is 5 years more than the age of B.
The age of B is 2 times the age of C.
If the age of C is 16 years, what is the age of A?
We can convert these statements into mathematical equations:
A = B + 5
B = 2C
C = 16
Therefore,
B = 2 × 16 = 32
A = 32 + 5 = 37
Answer: 37 years
For more detailed formulas, concepts, shortcuts and solved examples, explore our Age Formula and Concepts with Examples page.
Age Problems Questions
In this section, we will solve different types of Age Problems and learn how to apply age formulas and concepts to real questions.
The section covers questions ranging from easy to medium and difficult levels, helping aspirants understand how statements given in a question can be converted into mathematical equations and solved step by step.
For detailed questions, answers and solutions, explore our Age Problems Questions with Answers & Solutions section.
Age Problems Practice
This page is a dedicated practice section where Age Problems are presented in different formats, including MCQs, True/False, Fill in the Blanks and Word Problems. These questions will help aspirants strengthen their understanding and improve their ability to apply age concepts and formulas to different types of problems.
The questions range from easy to challenging levels and are designed to help aspirants become more confident in solving exam-type Age Problems.
Try this simple practice question:
Example 3
Q. A father is 24 years older than his son. If the son is 12 years old, what is the present age of the father?
Answer: 36 years
To test your Age Problems concepts, explore our detailed Age Problems Practice section and start solving the questions.
Remember: Don’t jump to the answers. Read the question carefully, identify the age relationships, form the required equations, and solve the problem yourself before checking the answer or solution.
Age Problems PYQs
This section covers Previous Year Questions (PYQs) from SSC, RRB, Defence, Police, Banking and other competitive examinations. To make them more engaging and relatable for MathsByNITian, we may modify names and numbers while retaining the underlying concepts and question patterns.
The PYQs are solved using the Age Problems formulas and concepts covered above. We strongly recommend that aspirants attempt each question themselves before checking the solution. If a question is difficult, revisit the relevant concepts and formulas before looking at the solution.
Example 4:
The ages of two RRB NTPC coaching-centre aspirants, A and B, are in the ratio of 9 : 8, respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their present ages? (Bank PO)
Can you solve it?
This question is solved step by step in our Age Problems PYQs section.
For more PYQs, explore our Age Problems PYQs SSC, RRB, Banking & Defence Exams section.
Important Age Problem Types
Present Age
Apsara is 2 years older than her brother. If her brother is 17 years old, how old is Apsara now?
Past Age
Apsara is 19 years old. Her brother is 2 years younger than her. How old was her brother 3 years ago?
Future Age
Apsara’s brother is 17 years old and is 2 years younger than her. How old will Apsara be 5 years from now?
Age Difference
Apsara is 5 years older than her brother. If her brother is 17 years old, what is Apsara’s present age?
Ratio of Ages
The present ages of Apsara and her brother are in the ratio 5 : 3. If Apsara is 25 years old, what is her brother’s present age?
Average Age
The average age of Apsara and her brother is 20 years. If Apsara is 22 years old, what is her brother’s age?
Family/Parent-Child Problems
Apsara’s father is 28 years older than her. If Apsara is 16 years old, what is her father’s present age?
Age-Based Equations
Apsara’s age is 4 years more than twice her brother’s age. If her brother is 12 years old, what is Apsara’s age?
How to Prepare Age Problems for Competitive Exams
Read the question carefully. Don’t be in a hurry, as Age Problems can be easily misinterpreted.
Identify the age relationships and form the required equation.
Substitute the values and simplify step by step.
Cross-check your answer with the conditions given in the question.
Follow the complete learning sequence. Learn the concepts and formulas first, then solve questions, practice, and finally attempt PYQs.