Problems on ages

Problems on Ages is a topic that is covered not so frequent in MBA exams. Problems on ages are important because MBA aspirants need to have the problem-solving skills to recognize what is the critical data that is needed to solve problems fast. The type of questions that come under is the calculation of one’s age given some hints/ ages of other people that are related.

Below, the details about Problems on ages under QA for CMAT is given: –


Problems on ages
YearNo of QuestionsGood attemptDifficulty


List of Concepts in that Chapter

The list of concepts that should be known by students are as follows: –

  • If the present age of a person is x, then n times the present age of that person=nx
  • If the present age of a person is x, then the age of that person n years later=x+n
  • If the present age of a person is x, then the age of that person n years ago=x-n
  • The ages of two people are in the ratio a:b, then their ages will be ax and by respectively
  • If the current age of a person is x, then 1/nth age of that person=x/n

Details on This Page

Some Sample Questions for Preparation

Some of the important questions on ages that can be useful for preparation are: –

1. The present age of the father is 5 times the age of his son. Five years ago, the age of the Father was ten times the age of his son at that time. How old is the father at present?


Let F and S be the current ages of the father and son respectively.

From the first statement: F = 5 S

From the second statement:

F – 5 = 10(S – 5).

So F – 5 = 10S – 50 or F = 10S – 45

Combining this last equation with the first:

5S = 10S – 45

=>> 45 = 5S (adding 45 to both sides and subtracting 5S from both sides)

Dividing by 5 gives us 9 = S

So the father is 45 and the son is 9.

Five years ago they were 40 and 4.


2. Father’s age is 25 years more than the son’s age. Four years hence, the Fathers age will become 1 less than thrice the son’s age What is the father’s present age?


Son’s age  =x

Father’s age = x + 25

after 4 years son’s age = x + 4

after 4 years Father’s age = x + 29 or 3(x+4) – 1

x + 29  =  3x + 12 – 1

2x = 29 -11

x = 18/2 = 9


Father’s present age = 9 + 25 = 34years


3. Raj’s age is 4 times that of Dhiraj, his cousin. 3 years back, Raj was 5 times as old as Dhiraj. What is his present age?

Dhiraj’s age = x-3 years

Raj’s age = 4x-3 years.

That time, Raj’s age = 5 times Dhiraj’s age

∴ 4x-3 = 5(x-3)

4x-3 = 5x-15

∴ x = 12 years

Let us consider Dhiraj’s present age as x years

Raj’s present age is 4 times Dhiraj’s = 4x years

Dhiraj’s age=12 years

Raj’s age=12×4=48years


4. The ages of 10 students and their teacher are such that the average of the first 7 student’s age is 15 years; the average of the last three student’s age is 11 years. The average age of all the students and their teacher together is 15 years. Find the age of the teacher.

Step-by-step explanation:

The sum of the ages of students and teachers =11*15=165

The sum of first seven students age=7*15=105

The sum of last three students age=3*11=33

The sum of age of 10 students =105+33


Teacher age =165-138

=27 years


How to deal with the topic preparation

Level 1 

  • Students are supposed to have basic knowledge of ratios, averages, fractions to attempt such questions
  • Students should develop problem-solving skills to identify critical data and use them to find solutions 

Level 2 

  • Topics such as average age, age after n years, age before n years are important concepts that the student needs to be thorough on
  • The problems on ages in the QA section is one of the easiest sections to attempt if the students have done their preparation properly

Level 3

Students need to look into problems that use multiple concepts to find a solution. Try to answer questions from the advanced level of previous CAT papers, mock tests, and materials. And try to attempt these questions in a time-based manner. Taking too much time for advanced questions will be disadvantageous in cracking the exam. Finally, students need to practice as many questions as they can to get a hold of the concepts and find solutions fast. Practice will always help the student to crack the exam


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