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 solve problems of ages. So, here’s an insightful blog to provide you with tips to easily crack such types of questions in a competitive exam.

**Also Read: Tips to Crack Competitive Exams**

##### This Blog Includes:

## Problems on Ages: Concept and Basics

The age-based tasks in the quantitative aptitude section are brain teasers, which may appear complicated at first but are simple to answer when tackled step by step.

Questions from this section are typically asked for 2-3 marks, but age-based questions may be asked as part of the data sufficiency or** data interpretation** sections. As a result, it is critical that each candidate understands the concept.

The questions, as the name implies, are word problems based on the ages of the people. They can be asked in either equation or direct form.

**Also, Read: Analytical Reasoning For Competitive Exams**

## How to Solve Problems on Ages?

As **aptitude questions** on age are frequently asked in almost every competitive exam, be it the **GMAT, GRE, SAT, CAT,** etc., applicants should 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 is 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’s 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**

## Important Formulas

Here are a few formulas linked to age problems that may help you answer the questions faster and acquire a better understanding of the concept:

- If you are assuming the current age to be x, then the age after n years will be (x+n) years.
- If you are assuming the current age to be x, then the age before n years will be (x-n) years.
- If the age is given in the form of a ratio, for example, p:q, then the age shall be considered as qx and px
- If you are assuming the current age to be x, then n times the current age will be (x×n) years
- If you are assuming the current age to be x, then 1/n of the age shall be equal to (x/n) years

## Sample Problems on Ages

Questions on age 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? **

- 16.2 years
- 7.7 years
- 8.7 years
- 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.**

- 25 years
- 26 years
- 31 years
- 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?**

- 10 years
- 15 years
- 20 years
- 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?**

- 12 years
- 15 years
- 20 years
- 22 years
- 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?**

- 11 years
- 13 years
- 15 years
- None of the above
- 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?**

- 4 years
- 8 years
- 10 years
- 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?**

- 24
- 27
- 40
- 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?**

- 40 years
- 32 years
- 33 years
- 45 years
- 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:**

- 14 years
- 19 years
- 33 years
- 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?**

- 16 years
- 18 years
- 20 years
- 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:**

- 19
- 29
- 39
- 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:**

- 5
- 10
- 15
- 20

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

- 12
- 14
- 22
- 10

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

- 36 years
- 38 years
- 40 years
- 42 years

## Best Books for Quantitative 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
- Mathematics by Rakesh Yadav
- 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

**Relevant Read: Word Problems on Arithmetic Operations**

## Tricks and Tips

Candidates who are unfamiliar with the concept and tend to either skip or incorrectly answer the age issues can benefit from the advice provided below. These hints may assist you in answering the question by following a predetermined pattern and then determining the answer.

- The most important thing is to attentively study the question and gradually develop the equation that will help you answer it.
- Basic operations such as addition, subtraction, multiplication, and division will assist a candidate in arriving at an answer, and no complex computations are necessary to answer such problems.
- Arrange the given values accurately in an equation by assigning variables to the unknown values.
- Once the equation is complete, solve it to obtain the answer.
- The final step is to double-check the solution by plugging it into the equation to confirm that no errors were made while calculating.

**Also, Read: Multiplication and Division Word Problems**

**Also Read:**

**Mensuration Formulas for Competitive Exams****Seating Arrangement Questions for Competitive Exams****Percentage Questions for GMAT****Number Series Questions for Competitive Exams****Time and Distance Questions for GMAT****Simplification Questions for GMAT****Ratio and Proportion Problems for GMAT****GMAT Profit and Loss Questions****GMAT Problems on Trains**

## FAQs

**Q1. What is the formula for the problem of age?**

Ans. If the age is supplied in the form of a ratio, such as p:q, the age is regarded as qx and px. If you assume the current age is x, then n times the current age equals (xn) years. If you assume that the current age is x, then 1/n of the age is (x/n) years.

**Q2. What is the age ratio?**

Ans. One indicator of the predictive potential of an aptitude test is calculated by dividing the student’s chronological age at one administration of a test by his or her age at a later administration of the same test.

**Q3. What is the best age for an aptitude test?**

Ans. Surprisingly, the aptitude testing technique is frequently the same regardless of age or educational level. Experts advocate delaying aptitude testing until a child is at least 15 years old, but this isn’t only for teenagers. Aptitude testing can be beneficial and informative at any age.

We understand that **preparing for the competitive exam** can be a stressful process but with the help of the **study abroad** 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.