In the previous chapter, we introduced the basics of Age Problems. In this chapter, we will learn the important Age formulas and concepts, understand how they are applied, and solve examples based on them.
Let us begin with the basic Age Problems formulas and concepts.
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Basic Age Formulas and Concepts.
1. Present Age
We already saw a type of question on the Present Age in our previous chapter. Here, we will understand a basic age relationship and how to find the present age from the information given in a question.
Example 1:
An RRB aspirant A is 3 years older than another RRB aspirant B. If B is 29 years old, how old is A?
Let the present age of A be x.
Since A is 3 years older than B:
x = 29 + 3
x = 32
Basic Present-Age Formula
Age of Older Person = Age of Younger Person + X
where X = the age difference between the two persons.
Therefore, A’s present age is 32 years.
2. Age N Years Ago
There may be questions where we have to find a person’s age a certain number of years ago. In such questions, we first need to find the person’s present age and then calculate their age in the past.
For example, if a person is 25 years old now, their age 2 years ago was:
25 − 2 = 23 years
However, in competitive exams, such questions are usually based on age relationships between two or more people, so we first need to understand the given relationships and find the required present age. Check the below example.
Example 2:
There are two SSC aspirants, A and B. A is 3 years younger than B. B was 26 years old 5 years ago. What was A’s age 2 years ago?
Let B’s present age be x.
Since B was 26 years old 5 years ago:
x = 26 + 5 = 31
A is 3 years younger than B:
A = 31 − 3 = 28
Therefore, A’s age 2 years ago:
28 − 2 = 26 years
Formula
Age N Years Ago = Present Age − N
where N = the number of years in the past.
3. Age N Years From Now
We may come across questions where we have to calculate a person’s age in the future. If we know the person’s present age, we can easily find their age after a given number of years.
Example 3:
If Apsara is 18 years old now, how old will she be 3 years from now?
18 + 3 = 21 years
Let us see a slightly more complex example:
Two bank employees, A and B, have an age difference of 2 years. A is younger than B. If B is currently 31 years old, how old will A be 2 years from now?
Solution:
Present age of A:
31 − 2 = 29 years
Age of A after 2 years:
29 + 2 = 31 years
Answer: 31 years
Formula
Age N Years From Now = Present Age + N
where N = the number of years in the future.
4. Age difference
We may also come across questions where we have to find the age difference between two people. For example, if one aspirant is 28 years old and another is 30 years old, their age difference is:
30 − 28 = 2 years
However, competitive-exam questions may provide the information in a more indirect way.
Example 4:
Aspirants A and B joined as RRB ALP employees 5 years ago. A was 29 years old when he joined. A was 3 years younger than B when they joined. What is the age difference between them?
Since A was 3 years younger than B:
Age Difference = 3 years
The 5 years that have passed do not change the age difference between them.
Answer: 3 years
Formula
Age Difference = Older Person’s Age − Younger Person’s Age
And the age difference between two people remains constant over time.
5. Age Ratio
In Age Problems, we may also come across questions where the ages of two or more people are given in a ratio.
Example 5:
The ages of aspirants A and B are in the ratio 3 : 5. If A’s age is 21 years, what is B’s age?
Let their ages be 3x and 5x.
Since A’s age is 21:
3x = 21
x = 7
Therefore:
B’s age = 5 × 7 = 35 years
Answer: 35 years
Basic Age-Ratio Formula
If the ages of A and B are in the ratio m : n, their ages can be represented as:
A = mx and B = nx
where x = the common multiplier.
6. Average Age
We have already solved questions related to Average Age in our Average section. We have also introduced this concept in the Age Problems chapter. Now, let us understand how the average-age concept can be applied to an Age Problem.
Example 6:
The average age of Apsara and her brother is 20 years. If Apsara is 22 years old, how old is her brother?
First, find the total age of both:
Total Age = Average Age × Number of People
Total Age = 20 × 2 = 40 years
Therefore, her brother’s age:
Brother’s Age = 40 − 22 = 18 years
Answer: 18 years
Average Age Formula
Average Age = Total Age ÷ Number of People
Therefore:
Total Age = Average Age × Number of People
7. Age Ratio Before/After N Years
We may also come across questions where the ratio of the ages of two people before or after a certain number of years is given or needs to be calculated.
Example 7:
The present ages of two RRB aspirants, A and B, are in the ratio 2 : 3. If A is 24 years old, what will be the ratio of their ages after 6 years?
Let their present ages be:
A = 2x
B = 3x
Since A is 24 years old:
2x = 24
x = 12
Therefore:
B = 3 × 12 = 36 years
After 6 years:
A = 24 + 6 = 30 years
B = 36 + 6 = 42 years
Therefore:
Ratio = 30 : 42 = 5 : 7
Answer: 5 : 7
Formula
If the present ages of A and B are in the ratio m : n, their ages can be represented as:
A = mx, B = nx
After N years:
Ratio = (mx + N) : (nx + N)
N years ago:
Ratio = (mx − N) : (nx − N)
where x = common multiplier and N = number of years before or after the present.
8. Family / Parent-Child Age Problems
We often come across family and parent-child age problems in competitive exams. These questions usually give age relationships between parents and children, and we need to use those relationships to find an unknown age.
Example 8:
In a family, the father’s age is twice the age of his son. The mother is 35 years old and is 5 years younger than her husband. What is the age of the son?
Mother’s age = 35 years
Since the mother is 5 years younger than the father:
Father’s age = 35 + 5 = 40 years
The father’s age is twice the son’s age:
40 = 2 × Son’s age
Son’s age = 20 years
Answer: 20 years
Formula / Equation
If the father’s age is twice the son’s age:
Father’s Age = 2 × Son’s Age
More generally, if one person’s age is n times another person’s age:
Older Person’s Age = n × Younger Person’s Age
9. Age-Based Equations
Let us learn how to convert age-related statements into mathematical equations.
Suppose the question says:
The age of Apsara is 5 years more than her brother’s age.
This can be represented as:
Age of Apsara = Age of Brother + 5
We add 5 because the question says Apsara is 5 years older than her brother.
Similarly, if the question says:
The age of Apsara is 5 years less than her brother’s age.
Then:
Age of Apsara = Age of Brother − 5
We subtract 5 because Apsara is 5 years younger than her brother.
Basic Rule
“More than” → Add
“Less than” → Subtract
10. Mixed Age Problems
Some competitive-exam Age Problems combine two or more age concepts in a single question. Such questions require us to identify each relationship and apply the relevant formulas step by step. You can see how these concepts are applied in different exam-level questions in our Age Questions with Answers & Solutions section.
Example 9:
The ages of two RRB NTPC aspirants are in the ratio 3 : 5. If the age of the younger aspirant is 30 years, what will be the age difference between them after 6 years?
Let their present ages be:
Younger = 3x
Older = 5x
Since the younger aspirant is 30 years old:
3x = 30
x = 10
Therefore:
Older age = 5 × 10 = 50 years
Present age difference:
50 − 30 = 20 years
After 6 years:
Younger = 36 years
Older = 56 years
Age difference:
56 − 36 = 20 years
Answer: 20 years
Practice Questions
- The average age of the father and mother in an RRB aspirant’s family is 38 years. The average age of the father, mother and their only son is 30 years. What is the age of the son?
Answer: 14 years.
- The average age of IRCTC Catering employees at a railway station was 18 years. When 4 employees, whose average age was 15 years, joined the team, the average age decreased by 6 months. How many employees were there originally?
Answer: 20 employees
For more practice, explore our Age Problems Practice Questions and test your understanding of the concepts covered above.
What We Learned in Age Formulas & Concepts
In this chapter, we learned the important Age formulas and concepts used in competitive-exam questions. We learned how to:
- Find the present age using age relationships.
- Calculate age N years ago and N years from now.
- Find the age difference and understand that it remains constant over time.
- Solve problems involving age ratios.
- Calculate average age and total age.
- Find age ratios before or after N years.
- Solve family and parent-child age problems.
- Convert age-related statements into mathematical equations.
- Solve mixed age problems by combining multiple age concepts.
Related Topics to Age Formulas
- Ratio & Proportion → Important for age-ratio problems.
- Percentage → Useful when age relationships involve percentage-based changes.
- Algebra → Helps in forming and solving age-based equations.
- Average→ Useful for average-age problems and combined age calculations.
- Age Concepts
- Age Questions with Answers & Solutions
- Age PYQs SSC, RRB, Banking & Defence Exams