# Problems on Ages in Competitive Exams

Every year thousands of students appear for competitive exams. Be it for pursuing higher education abroad or to grab a government position in India, competitive exams are the entry gates to move further in your career. When it comes to gearing up for these exams, there is a common possibility that sometimes your preparation might not match the level of your performance. However, you should not let your efforts go in vain. If you are sincerely working to achieve your goal, all these are just mere obstacles that should barely affect you. If we take a look at any competitive exam, we always find that there is one ‘quantitative and logical aptitude’ section testing your logical ability to solve mathematical problems. Ever thought about how to ace this particular section? It’s quite easy if you have an idea about the different topics covered in this section. Few of the prominent questions are asked to solving problems on ages. So, here’s an insightful blog to provide you with the tips to easily crack such types of questions in a competitive exam.

Also Read: Tips to Crack Competitive Exams

## How to Solve Problems on Ages?

As aptitude questions on ages are frequently asked in almost every competitive exam, be it the GMAT, GRE, SAT, CAT, etc., applicants should definitely know how to solve these within minimum time.

To make this easier for you, let’s take a look at some of the basic mathematical concepts and tricks related to problems on ages:

• If the present age of a person be X, then
• Age after n years = X + n
• Age n years ago = X – n
• n times the present age = nX
• If ages in the numerical are mentioned in the ratio A:B, then A:B will be AX and BX
• If the sum of ages is X and Y and the ratio of their ages is p:q respectively, then you can determine the age of Y by using the formula shown below:
• Age of Y = Ratio of Y/ Sum of ratios x sum of ages
• Age of Y = q/ (p+q) x A

## Points to Remember

• After reading the problems on ages, assume the unknown age to be some variable, let say ‘X’.
• Convert the statements in the question into mathematical equations.
• Calculate the variable by solving the equations and the obtained value must satisfy the conditions given in the problem.

Also Read: Maths for Competitive Exams

## Sample Problems on Ages

Questions on ages in a competitive exam are classified into four categories. Below are some examples to understand the concept explained above:

#### Type 1 – Calculate the Present Age

What is John’s present age, if 10 years later his age will be 5 times his age 6 years ago?

1. 16.2 years
2. 7.7 years
3. 8.7 years
4. 10 years

Correct option is 4
Let John’s present age be X
John’s age 6 years ago = (X-6)
John’s age 10 years later = (X+10)
We are given that John’s age after 10 years (x + 10) is 5 times his age 5 years ago (x-6).

Therefore,
(x +10) = 5 (x-6)
Solving the equation, we get
x + 10 = 5(x-6)
x+10 = 5x – 30
4x = 40
x= 10

#### Type 2 – Determine the Ages in Ratio Form

One year ago, the ratio of Parul and Atima’s age was 5:6 respectively, after 4 years, the ratio becomes 6:7. Find the present age of Atima.

1. 25 years
2. 26 years
3. 31 years
4. 35 years

Correct option is 3

Hint: If ages in the numerical are mentioned in ratio A: B, then we assume ages as Ax and Bx
We are given the age ratio of Parul and Atima = 5:6
One year ago, their age was 5x and 6x. Hence at present, Parul’s age = 5x+1 and Atima’s age = 6x+1
After 4 years, Parul’s age = (5x+1) + 4 = (5x + 5)
Atima’s age =  (6x+1) + 4 = (6x + 5)
After 4 years, this ratio becomes 6:7

Therefore,
Parul’s age/6 = Atima’s age/7
(5x + 5) /  (6x + 5) = 6/7
7 (5x + 5) = 6 (6x + 5)
35x + 35 = 36x + 30
36x – 35x = 35 – 30
X = 5

Parul’s present age = (6x+1) = (6×5+1) = 31 years
Atima’s present age = (5x+1) = 5×5+1) = 26 years

#### Type 3 – Determine a Person’s Age Before x Years

Shivani is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4:6?

1. 10 years
2. 15 years
3. 20 years
4. 25 years

Correct option is 3

Let us assume x years ago
At present Shivani is 60 years old and Ritu is 80 years old.
X years ago : Shivani’s age = (60-x) and Ritu’s age (80-x)
Ratio of their ages x years ago was 4:6
(60-x) / (80-x) = 4/6
6 (60-x) = 4 (80-x)
360-6x = 320-4x
6x – 4x = 360 – 320
2x = 40
x = 20

Therefore, 20 years ago their age ratio was 4:6

## Age Problem Questions

Here are some same questions related to Problems on Age for you to practise and learn.

Q. The present age of Aradhana and Aadrika is in the ratio 3:4. 5 years back, the ratio of their ages was 2:3. What is the present age of Aradhana?

1. 12 years
2. 15 years
3. 20 years
4. 22 years
5. 10 years

Q.  If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?

1. 11 years
2. 13 years
3. 15 years
4. None of the above
5. Cannot be Determined

Q. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

1. 4 years
2. 8 years
3. 10 years
4. None of these

Q. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?

1. 24
2. 27
3. 40
4. Can’t be determined

Q. A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

1. 40 years
2. 32 years
3. 33 years
4. 45 years
5. 22 years

Q. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:

1. 14 years
2. 19 years
3. 33 years
4. 38 years

Q. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?

1. 16 years
2. 18 years
3. 20 years
4. Can’t be determined

Q. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is:

1. 19
2. 29
3. 39
4. 49

Q. The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

Q. The sum of the present ages of a father and his son is 60 years. five years ago, a father’s age was four times the age of the son. so now the son’s age will be:

1. 5
2. 10
3. 15
4. 20

Q. Rajeev’s age after 15 years will be 5 times his age 5 years back. What is the present age of rajeev?

1. 12
2. 14
3. 22
4. 10

Q. A person’s present age is two-fifth of the age of his mother. (Xanax) After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

1. 36 years
2. 38 years
3. 40 years
4. 42 years

## Best Books for Quantatitive Reasoning

Here is a list of books you can refer to for the topic- Problems on Age and use for competitive exams:

• Quantitative aptitude by RS Agarwal
• How to Prepare for Quantitative Aptitude for the CAT by Arun Sharma
• Objective mathematics by Fastrack
• Quantitative aptitude by Arun Sharma and Manorama Sharma
• Quantitative aptitude By Pearson Guide & Quantitative aptitude by Sarvesh K. Verma
• Shortcuts in Quantitative Aptitude for Competitive Exams by Disha Publication

We understand that preparing for the competitive exam can be a stressful process but with the help of the experts at Leverage Edu you can come up with a plan to tackle such problems on ages and other challenges so that nothing comes between you and your ambitions.

Every year thousands of students appear for competitive exams. Be it for pursuing higher education abroad or to grab a government position in India, competitive exams are the entry gates to move further in your career. When it comes to gearing up for these exams, there is a common possibility that sometimes your preparation might not match the level of your performance. However, you should not let your efforts go in vain. If you are sincerely working to achieve your goal, all these are just mere obstacles that should barely affect you. If we take a look at any competitive exam, we always find that there is one ‘quantitative and logical aptitude’ section testing your logical ability to solve mathematical problems. Ever thought about how to ace this particular section? It’s quite easy if you have an idea about the different topics covered in this section. Few of the prominent questions are asked to solving problems on ages. So, here’s an insightful blog to provide you with the tips to easily crack such types of questions in a competitive exam.

Also Read: Tips to Crack Competitive Exams

## How to Solve Problems on Ages?

As aptitude questions on ages are frequently asked in almost every competitive exam, be it the GMAT, GRE, SAT, CAT, etc., applicants should definitely know how to solve these within minimum time.

To make this easier for you, let’s take a look at some of the basic mathematical concepts and tricks related to problems on ages:

• If the present age of a person be X, then
• Age after n years = X + n
• Age n years ago = X – n
• n times the present age = nX
• If ages in the numerical are mentioned in the ratio A:B, then A:B will be AX and BX
• If the sum of ages is X and Y and the ratio of their ages is p:q respectively, then you can determine the age of Y by using the formula shown below:
• Age of Y = Ratio of Y/ Sum of ratios x sum of ages
• Age of Y = q/ (p+q) x A

## Points to Remember

• After reading the problems on ages, assume the unknown age to be some variable, let say ‘X’.
• Convert the statements in the question into mathematical equations.
• Calculate the variable by solving the equations and the obtained value must satisfy the conditions given in the problem.

Also Read: Maths for Competitive Exams

## Sample Problems on Ages

Questions on ages in a competitive exam are classified into four categories. Below are some examples to understand the concept explained above:

#### Type 1 – Calculate the Present Age

What is John’s present age, if 10 years later his age will be 5 times his age 6 years ago?

1. 16.2 years
2. 7.7 years
3. 8.7 years
4. 10 years

Correct option is 4
Let John’s present age be X
John’s age 6 years ago = (X-6)
John’s age 10 years later = (X+10)
We are given that John’s age after 10 years (x + 10) is 5 times his age 5 years ago (x-6).

Therefore,
(x +10) = 5 (x-6)
Solving the equation, we get
x + 10 = 5(x-6)
x+10 = 5x – 30
4x = 40
x= 10

#### Type 2 – Determine the Ages in Ratio Form

One year ago, the ratio of Parul and Atima’s age was 5:6 respectively, after 4 years, the ratio becomes 6:7. Find the present age of Atima.

1. 25 years
2. 26 years
3. 31 years
4. 35 years

Correct option is 3

Hint: If ages in the numerical are mentioned in ratio A: B, then we assume ages as Ax and Bx
We are given the age ratio of Parul and Atima = 5:6
One year ago, their age was 5x and 6x. Hence at present, Parul’s age = 5x+1 and Atima’s age = 6x+1
After 4 years, Parul’s age = (5x+1) + 4 = (5x + 5)
Atima’s age =  (6x+1) + 4 = (6x + 5)
After 4 years, this ratio becomes 6:7

Therefore,
Parul’s age/6 = Atima’s age/7
(5x + 5) /  (6x + 5) = 6/7
7 (5x + 5) = 6 (6x + 5)
35x + 35 = 36x + 30
36x – 35x = 35 – 30
X = 5

Parul’s present age = (6x+1) = (6×5+1) = 31 years
Atima’s present age = (5x+1) = 5×5+1) = 26 years

#### Type 3 – Determine a Person’s Age Before x Years

Shivani is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4:6?

1. 10 years
2. 15 years
3. 20 years
4. 25 years

Correct option is 3

Let us assume x years ago
At present Shivani is 60 years old and Ritu is 80 years old.
X years ago : Shivani’s age = (60-x) and Ritu’s age (80-x)
Ratio of their ages x years ago was 4:6
(60-x) / (80-x) = 4/6
6 (60-x) = 4 (80-x)
360-6x = 320-4x
6x – 4x = 360 – 320
2x = 40
x = 20

Therefore, 20 years ago their age ratio was 4:6

## Age Problem Questions

Here are some same questions related to Problems on Age for you to practise and learn.

Q. The present age of Aradhana and Aadrika is in the ratio 3:4. 5 years back, the ratio of their ages was 2:3. What is the present age of Aradhana?

1. 12 years
2. 15 years
3. 20 years
4. 22 years
5. 10 years

Q.  If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?

1. 11 years
2. 13 years
3. 15 years
4. None of the above
5. Cannot be Determined

Q. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

1. 4 years
2. 8 years
3. 10 years
4. None of these

Q. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?

1. 24
2. 27
3. 40
4. Can’t be determined

Q. A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

1. 40 years
2. 32 years
3. 33 years
4. 45 years
5. 22 years

Q. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:

1. 14 years
2. 19 years
3. 33 years
4. 38 years

Q. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?

1. 16 years
2. 18 years
3. 20 years
4. Can’t be determined

Q. In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is:

1. 19
2. 29
3. 39
4. 49

Q. The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

Q. The sum of the present ages of a father and his son is 60 years. five years ago, a father’s age was four times the age of the son. so now the son’s age will be:

1. 5
2. 10
3. 15
4. 20

Q. Rajeev’s age after 15 years will be 5 times his age 5 years back. What is the present age of rajeev?

1. 12
2. 14
3. 22
4. 10

Q. A person’s present age is two-fifth of the age of his mother. (Xanax) After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

1. 36 years
2. 38 years
3. 40 years
4. 42 years

## Best Books for Quantatitive Reasoning

Here is a list of books you can refer to for the topic- Problems on Age and use for competitive exams:

• Quantitative aptitude by RS Agarwal
• How to Prepare for Quantitative Aptitude for the CAT by Arun Sharma
• Objective mathematics by Fastrack