In this article, we are going to cover the key concepts of problems on ages along with types of questions, tips and tricks and questions with solutions that will be beneficial for students in their exam preparation.

What are Problems in Ages?

Problems on age are one of the applications of linear equations. When solving problems on ages, the ages of two or more persons are compared with the ratio, fraction or percentage. Then in that case, we could correlate the entire situation to the short tricks of ratio. The main challenge in handling the questions on problems on ages is your ability to bifurcate which data is of present and which one is of past and which one is of future.

Maths Notes Free PDFs

Problems on Ages-Concepts and Basics 

The types of questions from problems on ages asked in different government exams under aptitude section are as follows:

Ratio and Sum of Ages Given

If the ratio of present age of A and B is x : y and their sum of present age is P, then

A = x / (x + y) × P and B = y / (x + y) × P

Ratio and Product of Ages Given under Problems on Ages

In this type of age-related question, the ratio and the product of ages will be given. Candidates have to use those to conclude the final result.

Ratio of Present and Future Ages Given

In this type of age-related question, the ratio of present and future ages will be given. Candidates have to use those to conclude the final result.

Ratio of Past and Present Ages Given

In this type of age-related question, the ratio of past and present ages will be given. Candidates have to use those to conclude the final result.

Age-related questions can seem tricky, but if you know a few simple rules, they become very easy to solve. Let’s go through the most important ones in a simple way:

Future Age:

To know someone’s age after a few years, you just need to add the number of years to their current age.

Formula: Future Age = Present Age + Number of Years = x + n.
For example, if Riya is 10 years old now, then after 5 years, she will be 10 + 5 = 15 years old.

Past Age:

To find out how old someone was a few years ago, subtract the number of years from their current age.

Formula: Past Age = Present Age – Number of Years = x – n

For example, if Arjun is 20 years old now, then 4 years ago, he was 20 – 4 = 16 years old.

Age in Ratios:

Sometimes, you’ll get age questions in a ratio like 2:3. This just means that if one person’s age is 2 parts, the other’s is 3 parts.

Formula: If ratio = p : q Then, Ages = p × x and q × x

Let’s say their ages are 2x and 3x. You can find x using other information in the question.

Multiple of an Age:

If it says one person is a certain number of times older than another, just multiply the smaller age by that number.

Formula:Age = n × x

If Seema is 3 times as old as her brother who is 5, then Seema is 3 × 5 = 15 years old.

Fraction of an Age:

To find a portion of someone’s age, divide their age by the given number.
Formula:Fraction of Age = x ÷ n

If someone is 24 years old, then one-fourth of their age is 24 ÷ 4 = 6 years.

Tips & Tricks to Solve Problems on Ages 

 Candidates can find different problems on ages tricks and tips from below for solving the questions.

Tip 1: If the current age is x, then n times the age is nx.

Tip 2:If the current age is x, then the age n years later/hence = x + n

Tip 3: If the current age is x, then age n years ago = x – n

Tip 4: The ages in a ratio a:b will be ax and bx

Tip 5: If the current age is x, then 1/n of the age is x/n

Once you’ve mastered Problems on Ages, you can attempt problems on ages MCQs.

Sample Questions-Problems on Ages 

Question 1: If the ratio of present age of Ashutosh and Vishal is 9 : 4 and their sum of present age is 52 years, find the present age of Vishal.

Solution: Let, age of Ashutosh be 9x and age of Vishal be 4x Then, sum of both ages = 9x + 4x = 13x

⇒ 13x = 52

⇒ x = 4 years

∴ Age of Vishal = 4x = 4 × 4 = 16 years

Question 2: Product of present age of Ram and Lakshaman is 2223 years and their present age ratio is 19:13. Find the difference in age of Ram and Lakshaman.

Solution: Let, age of Ram be 19x and age of Lakshaman be 13x Then, product of their ages = 19x × 13x = 247×2

⇒ 247×2 = 2223

⇒ x2 = 9

⇒ x = 3

Hence, required difference = 19x – 13x = 6x = 6 × 3 = 18 years

Question 3: The ratio of present age A and B is 13:10. After 2.5 years their ratio will be 32:25 then find the present age of A.

Solution: Let, present age of A = 13x and present age of B = 10x According to question:

(13x + 2.5)/(10x + 2.5) = 32/25

⇒ (13x + 2.5) × 25 = (10x + 2.5) × 32

⇒ 325x + 62.5 = 320x + 80

⇒ 5x = 17.5

⇒ x = 3.5

Question 4: If 5 years ago, the ratio of age of Mradul and Love was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Love after 20 years.

Solution: Let, the present age of Mradul be x and the present age of Love be y.

Then, according to question (x – 5)/(y – 5) = ½

⇒ 2x – 10 = y – 5

⇒ x = (y + 5)/2———- (1)

Also, (x + 15)/(y + 15) = 5/6

⇒ 6x + 90 = 5y + 75

⇒ 6x + 15 = 5y

Putting value of x from equation 1, we get 3y + 15 + 15 = 5y

⇒ 2y = 30

⇒ y = 15

∴ Age of Love after 20 years = 15 + 20 = 35 years.

Question 5: Ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old the younger one, find their present age?

Solution: Let the age of an younger person be A

age of elder person = (A + 16)

According to the question, we have

3(A – 6) = (A + 16 – 6)

⇒ 3A – 18 = A + 10

⇒ 2A = 28

⇒ A = 14

∴ The younger and elder person age is 14 years old and 30 years old.

Question 6: Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?

Solution: 2 times the age of X = 3 times the age of Y

Difference between X and Y, 8 years back = 18 years

2X = 3Y

⇒ X : Y = 3 : 2

Let the present age of X and Y be 3R and 2R respectively

⇒ 3R – 2R = 18

⇒ R = 18

⇒ 3R = 3 × 18 = 54

∴ The present age of X is 54 years

Question 7: A person’s age is 3 times the age of his friend. The total of their ages is 64 years. Find the ages of the person and his friend.

Solution: A person’s age is 3 times the age of his friend.

The total of their ages is 64 years.

Let the age of friend be x

Let the age of person be 4x

According to the question, we have

Total of their ages = x + 3x

Thus,

x + 3x = 64

4x = 64

x = 16

∴ The age of the friend = 16,

The age of the person = 16 × 3 = 48

∴ The age of the person and friend is 48 and 16 years.

Question 8: The mean of the ages of father and his son is 27 years. After 18 years, the father will be twice as old as his son. Their present ages are?

Solution: Let the ages of father and son be x and y respectively,

Then the mean ages of father and son be (x + y)/2,

According to the given conditions

(x + y)/2 = 27

⇒ (x + y) = 54

⇒ x + y = 54 —eqn (1)

After 18 years

x + 18 = 2(y + 18)

⇒ x + 18 = 2y + 36

⇒ x – 2y = 18 —eqn (2)

Solving equations 1 & 2 we get

x = 42 & y = 12

Hence, age of father is 42 and son is 12

Question 9: The ages of A, B and C together is 65 years. B is 2/3 of A and C is 9 years older than A. Then, what is the ratio of the respective age of C, A and B?

Solution: The ages of A, B and C together = 65

Let age of A = x

Age of C = x + 9

Age of B = 2x/3

Let the age of A be x years

The ages of A, B and C together = 65

According to the question,

⇒ x + x + 9 + 2x/3 = 65

⇒ (3x + 3x + 27 + 2x)/3 = 65

⇒ 8x + 27 = 65 × 3

⇒ 8x = 195 – 27

⇒ x = 168/8

⇒ x = 21

A’s age = 21

B’ age = 2x/3

⇒ 2 × 21/3

⇒ 14

C’ age = x + 9

⇒ 21 + 9

⇒ 30

The ratio of the respective age of C, A and B = 30 : 21 : 14

∴ The ratio of the respective age of C, A and B are 30 : 21 : 14.

Question 10: The present age of Ram is 5 times the age of his son. After 12 years the age of Ram will be twice the age of his son, find the present age of son.

Solution: Let the present age of ram and his son be R years and S years respectively.

R = 5S

R + 12 = 2 (S + 12)

Also, R + 12 = 2 (S + 12)

⇒ R = 2S + 12

Replacing R in terms of S we get,

5S = 2S + 12

⇒ S = 4 years

∴ the present age of son = 4 years.

Hence, (a) is the correct answer.

List of government exams where problems on ages questions are asked

Following is the list of government exams where problems on ages questions are asked under aptitude section.

• SBI PO, SBI Clerk, IBPS PO, IBPS Clerk
• SSC CGL, SSC CHSL, SSC MTS
• LIC AAO, LIC ADO
• RRB NTPC, RRB ALP
• UPSC
• MPSC
• KPSC
• BPSC
• WBPSC
• Other State-Level Recruitment Examinations

We hope you found this article informative and helpful regarding problems on ages, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation. For better practice, solve the below provided previous year papers and mock tests for each of the given entrance exam: