In this article, we will explain the main concepts of problem on ages, which is an important topic in arithmetic reasoning. Age problems usually ask about the current, past, or future age of a person or a group of people. You will also learn about the different types of age related questions, such as finding the difference between ages, working with ratios, or calculating the sum of ages. Along with this, the article provides useful tips and tricks to solve age problems quickly and accurately. To help with exam preparation, we have included several age problem questions with step-by-step solutions. By understanding these methods, students can easily tackle any age-related questions in competitive exams and improve their problem-solving skills in arithmetic reasoning.

What are Problems in Ages?

Problems on age are an important application of linear equations. These problems usually compare the ages of two or more people using a ratio, fraction, or percentage. To solve them, we often use simple calculations based on these relationships. The main challenge is to understand which information relates to the present, the past, or the future. Once you separate the data correctly, you can set up equations to find the unknown ages. Practising these problems helps improve reasoning skills and makes it easier to solve any question about the ages of people in a clear, step-by-step way.

Problems on Ages-Concepts and Basics 

Age problem questions are a common topic in the aptitude section of government exams. These problems usually involve calculating the present, past, or future ages of individuals based on given conditions. They may also include relationships between the ages of two or more people, ratios, or differences. Understanding basic concepts, like the sum of ages or age differences, is essential to solve these questions accurately and quickly.

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 Problem Formulas 

Age-related problems may appear difficult, but they can be solved easily using a few simple formulas. Key rules include calculating a person’s present age, finding ages after or before a certain number of years, determining the difference between ages, and working with ratios of ages. By remembering these basic formulas and applying them step by step, you can quickly solve any age-related question in exams.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

Types of Problems on Ages

Age problems are a common topic in maths and reasoning. They focus on finding the age of a person or a group at a specific time—past, present, or future. These problems usually involve basic calculations like addition, subtraction, multiplication, or solving simple equations. Understanding the relationships between ages and using clear methods makes it easier to solve different types of age-related questions accurately.

1. Present Age Problems

• These questions ask for the current age of one or more people.
• Example: “John is 5 years older than Mary. If Mary is 12 now, how old is John?”

2. Past Age Problems

• These questions involve ages a few years ago.
• Example: “Ten years ago, a father was 5 times as old as his son. Find their current ages.”

3. Future Age Problems

• These are questions of ages after some years.
• Example: "In 5 years, Sara will be twice older than her brother. What are their ages now?"

4. Age Comparison Problems

• These are comparing the two or more people's ages.
• Example: "Father is 3 times older than his son. After 10 years, how will be their ratio of age?"

5. Ratio and Relationship Problems

• These issues represent ages as ratios or state family relationships such as father, son, or grandfather.
• For instance: "The ages of two friends are in the ratio 4:5. If the sum of their ages is 36, find each age."

6. Combined Age Problems

• These involve two or more types of calculations at the same time, like present and future ages together.
• Example: “A mother is 3 times older than her child. After 5 years, the mother’s age will be twice the child’s age. Find their current ages.”

Common Problem Types in Age Question in Maths

When solving age-related problems in maths, several types frequently appear in exams. These include calculating a person’s present, past, or future age, finding the difference between ages, working with ratios of ages, determining the sum of ages, and solving problems involving relationships between multiple people. Recognising these common types helps in choosing the right approach and applying formulas effectively to solve age questions quickly and accurately.

1, Simple Age Calculation

• These questions involve finding someone’s age based on a direct relationship with another person.
• Example: “A is 5 years older than B. If B is 12, what is A’s age?”

2. Sum of Ages

• In these problems, the total of the ages of two or more people is given, and you need to find each person’s age.
• Example: “The sum of A and B’s ages is 40. If A is twice as old as B, find their ages.”

3. Age Ratios

• These questions give the ratio of ages at a particular time. The ratio may change in the future or past.
• Example: “The present ages of A and B are in the ratio 3:2. After 5 years, what will the ratio be?”

4. Age Difference Scenarios

• Here, ages are related through a constant difference or a change in difference over time.
• Example: “The difference between father and son’s age is 25 years. How old will each be in 10 years?”

Tips & Tricks to Solve Problems on Ages 

Here are some useful tips and tricks to solve age-related problems quickly. By understanding key formulas, using age differences, and applying ratios or equations, candidates can solve questions accurately and save time in exams.

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 Problem 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 are 65 years. B is 2/3 of A, and C is 9 years older than A. Find the ratio of the ages of C, A, and B.

Solution:
Let the age of A = x years.
Then, age of B = 2x/3 and age of C = x + 9.

Total ages:
A + B + C = 65
x + 2x/3 + x + 9 = 65
Combine like terms:
x + x + 2x/3 + 9 = 65
(2x + 2x/3) + 9 = 65
Convert to fraction: (6x/3 + 2x/3) + 9 = 65
8x/3 + 9 = 65
8x/3 = 56
x = 56 × 3 / 8 = 21

So,
A = 21 years
B = 2x/3 = 2 × 21 / 3 = 14 years
C = x + 9 = 21 + 9 = 30 years

Ratio of C : A : B = 30 : 21 : 14.

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

Solution: Let the present age of Ram = R years, and the present age of his son = S years.

We know: R = 5 × S

After 12 years: R + 12 = 2 × (S + 12)

Substitute R = 5S:
5S + 12 = 2 × (S + 12)
5S + 12 = 2S + 24
5S – 2S = 24 – 12
3S = 12
S = 4

Answer: The present age of the son is 4 years.

Present age of Ram: R = 5 × 4 = 20 years

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: