Problems on Ages in Competitive Exams

Millions of students appear for competitive exams like JEE, NEET, CAT, GMAT, GRE, and SAT every year, aiming for higher education or government positions. Success in these exams often hinges on the quantitative aptitude section, which tests mathematical reasoning skills. Among the key topics, problems on ages stand out as frequently asked questions that can be tricky without a solid understanding.

This comprehensive guide explores the concepts, formulas, and methods to solve problems on ages efficiently. By practicing these techniques, you can approach age-related questions with confidence and boost your overall exam performance.

What Are the Basics of Problems on Ages?

Problems on ages are a fundamental part of the quantitative aptitude syllabus in competitive exams. These questions might seem puzzling at first, but breaking them down step by step reveals their straightforward nature, making them excellent for scoring marks.

In most competitive exams, problems on ages typically carry 2-3 marks and may integrate with data sufficiency or interpretation sections. Building a strong foundation is crucial for quick and accurate solutions.

These word problems revolve around the ages of individuals, often requiring you to set up equations based on given relationships. With clear concepts and consistent practice, you’ll master reading problem statements and applying logic effectively.

Essential Formulas for Problems on Ages

Formulas streamline the process of solving problems on ages, allowing for faster calculations during time-constrained exams. Familiarizing yourself with these basics helps in framing equations accurately and avoiding common errors. Below is a table of commonly used formulas:

Formula Type	Formula (if present age = x)	Example	Shortcut Tip
Future Age	Age after n years = x + n	If Rahul is 20, after 5 years → 25	Add directly to present age
Past Age	Age n years ago = x – n	If a girl is 15, 4 years ago → 11	Subtract from present age
Ratio of Ages	If ratio = p : q → Ages = p×k and q×k	If A : B = 2 : 3 and total = 50 → A=20, B=30	Multiply ratio by common factor
Multiple of Age	n times present age = n × x	If a boy is 12, twice his age → 24	Multiply directly
Fraction of Age	One-nth of age = x ÷ n	If a man is 40, one-fourth age → 10	Divide directly

Effective Methods to Solve Problems on Ages

Aptitude questions on ages are a regular feature in almost every competitive exam, whether it is GMAT, GRE, SAT, CAT, or other entrance tests. Since these questions need to be solved within a limited time, candidates should be familiar with the basic formulas and approaches.

To simplify the process, here are some fundamental concepts and tricks used in solving age-related problems:

1. Equation Method

The Equation Method is the most common approach, where you translate the word problem into mathematical equations using variables. It is useful when there are multiple people and conditions given.

Question: A father is three times as old as his son. After 12 years, the father will be twice as old as his son. Find their present ages.

Solution:

Let the son’s age = x.
Father’s age = 3x.
After 12 years → Father = 3x + 12, Son = x + 12.

Equation: 3x + 12 = 2(x + 12).
3x + 12 = 2x + 24 → x = 12.

Son = 12 years, Father = 36 years.

2. Ratio Method

Ratio Method is used when the relationship between ages is given in ratios and the total or the difference of ages is known. It saves time in direct ratio problems.

Question: The ratio of the present ages of A and B is 4:5. The sum of their ages is 72 years. Find their present ages.

Solution:

Sum of ratios = 4 + 5 = 9

A’s age = (4/9) × 72 = 32 years.
B’s age = (5/9) × 72 = 40 years.

3. Backtracking Method

In the Backtracking Method, you start from the conditions given in the past or future and work backward to find the present age. It is helpful in problems mentioning n years ago or after n years.

Question: Ten years ago, a mother was seven times as old as her daughter. Now, the mother is three times as old as her daughter. Find their present ages.

Solution:

Let daughter’s present age = x, Mother’s = 3x.
Ten years ago: Daughter = x – 10, Mother = 3x – 10.
Condition: 3x – 10 = 7(x – 10).
3x – 10 = 7x – 70 → 4x = 60 → x = 15.

Daughter = 15 years, Mother = 45 years.

4. Average Method

The Average Method works well when the average age and the total members are given. By multiplying the average by the number of members, you find the total sum of ages and solve further.

Question: The average age of a family of four members is 25 years. If the age of the father is 32 years, find the average age of the remaining three members.

Solution:

Total age of four = 25 × 4 = 100.
Father’s age = 32.
Remaining total = 100 – 32 = 68.
Average = 68 ÷ 3 = 22.67 years.

5. Assumption Method

In the Assumption Method, you assume one person’s age and build relationships directly. It is best for simple conditions like “twice,” “thrice,” or age differences.

Question: The present age of a brother is twice that of his sister. Five years ago, his age was three times hers. Find their present ages.

Solution:

Let sister’s age = x, Brother’s = 2x.
Five years ago → Brother = 2x – 5, Sister = x – 5.
Condition: 2x – 5 = 3(x – 5).
2x – 5 = 3x – 15 → x = 10.

Sister = 10 years, Brother = 20 years.

Explore: Arithmetic Questions to Put Your Skills to the Test

Sample Problems on Ages Based on Important Categories

Age-related questions are a staple in competitive exams, testing both arithmetic skills and logical reasoning. These problems can range from simple direct calculations to more complex scenarios involving multiple conditions, averages, or ratios. Understanding the different types of questions helps candidates approach them with confidence and accuracy.

To make this easier, we have aligned such questions into five main categories below, along with explanations for each:

Category 1: Single Person Age Problems

‘Single Person Age Problems’ questions focus on the age of just one individual, whether in the present, past, or future. They are generally straightforward and can be solved directly using basic formulas. Such problems are ideal for building confidence before tackling more complex scenarios. Try identifying the type of questions provided below.

Type 1: Present Age from Future/Past Conditions

1. Five years ago, the age of a boy was 10 years. What is his present age?
2. Ten years ago, a man was 25 years old. What is his age now?
3. A girl will be 18 years old after 5 years. Find her present age.
4. Four years ago, a father was 30 years old. How old is he now?
5. After 8 years, a boy will be 20 years old. Find his current age.
6. Five years from now, a mother will be 40 years old. Find her present age.
7. Ten years ago, a woman was three times the age of her daughter. If the daughter is now 20, what is the woman’s current age?
8. Seven years ago, a man was twice the age of his son. If the son is 14 years old now, how old is the man today?
9. A person’s age 6 years hence will be 25 years. Find his present age.
10. Twelve years ago, a boy was 8 years old. Find his present age.
11. Eight years ago, a man was half of what his age will be 8 years hence. Find his current age.
12. Ten years ago, a father was 12 times his son’s age. If the son is now 15, what is the father’s age?
13. After 4 years, a girl will be 5 times as old as she was 4 years ago. What is her current age?
14. Six years ago, a brother was four times his sister’s age. If the sister is 12 years old now, how old is the brother today?
15. Five years ago, the age of a man was one-fourth of what it will be after 5 years. Find his present age.
16. Four years from now, a man will be 5 times as old as he was 4 years ago. Find his current age.
17. A mother is 21 years older than her child. Six years ago, she was 5 times the child’s age. Find the present ages of both.
18. Ten years ago, a man’s age was half of what it will be in 10 years. Find his present age.
19. Three years ago, the age of a father was 7 times his son’s age. After 3 years, it will become 4 times. Find their current ages.
20. Four years ago, a person’s age was 3 times his son’s age. Four years hence, he will be twice his son’s age. Find their present ages.

Type 2: Age Relationship with Specific Time Frames

1. A father is 3 times as old as his son. If the son is 10 years old, find the father’s age.
2. A mother is twice the age of her daughter. If the daughter is 12, what is the mother’s current age?
3. A man is 24 years older than his son. If the son is 18, what is the man’s age?
4. The age difference between two brothers is 6 years. If the elder is 20, what is the younger’s age?
5. A father is 4 times the age of his son. After 10 years, their ages will differ by 30 years. Find their current ages.
6. A man is twice the age of his son. After 15 years, he will be 1.5 times his son’s age. Find their ages.
7. A mother is 5 times the age of her daughter. In 10 years, she will be 3 times her daughter’s age. Find their present ages.
8. The sum of the ages of a father and son is 50. If the father is 4 times the son’s age, find their ages.
9. The ratio of ages of two friends is 3:2. If the elder is 24, find the younger’s age.
10. The age difference between a brother and sister is 5 years. If the brother is 3 times the age of his sister, find both ages.
11. A father is 30 years older than his son. After 10 years, the father will be twice the son’s age. Find their ages.
12. A woman is 4 times the age of her son. After 20 years, their ages will be in the ratio 3:2. Find their present ages.
13. The ratio of ages of a man and his son is 7:3. After 5 years, the ratio becomes 2:1. Find their current ages.
14. A girl is twice as old as her brother. If the sum of their ages is 24, find their present ages.
15. A man is 28 years older than his son. After 4 years, the father will be 3 times the son’s age. Find their present ages.
16. The sum of ages of a father and son is 60 years. After 10 years, the father will be twice the son’s age. Find their present ages.
17. A father is 4 times as old as his son. 5 years ago, the ratio of their ages was 9:2. Find their present ages.
18. The ratio of ages of a brother and sister is 5:3. After 8 years, the ratio will become 7:5. Find their present ages.
19. The difference between ages of a mother and daughter is 21 years. After 6 years, the mother will be 5 times as old as her daughter. Find their present ages.
20. A man is 5 years older than his wife, and 15 years older than his son. If the wife is 30, find the man’s and son’s ages.

Category 2: Multiple Person Age Problems

‘Multiple Person Age Problems’ involve two or more individuals and usually explore age differences, ratios, or the total sum of ages. Solving these requires forming equations based on the relationships described in the question, testing both logical reasoning and calculation skills.

Check the examples below to see this category in action.

Type 1: Family Age Relationships

1. The sum of the ages of a father and his son is 60 years. If the father is 5 times as old as his son, find their present ages.
2. A mother is 4 times as old as her daughter. After 5 years, the mother will be 3 times as old. Find their present ages.
3. The age difference between a father and his son is 25 years. After 5 years, the father will be twice as old as his son. Find their present ages.
4. The sum of ages of a man, his wife, and their daughter is 90 years. If the man is twice the age of his wife and the wife is 3 times the age of the daughter, find their ages.
5. The ratio of ages of a father and son is 7:2. After 10 years, the ratio will be 9:4. Find their present ages.
6. A mother is 30 years older than her daughter. In 5 years, the mother will be 5 times her daughter’s age. Find their present ages.
7. The sum of the ages of two brothers is 40 years. If the elder brother is twice as old as the younger, find their ages.
8. A father’s age is 3 times the age of his son. In 15 years, the father will be twice as old. Find their present ages.
9. The ratio of ages of a brother and sister is 5:3. After 6 years, the ratio becomes 7:5. Find their present ages.
10. The difference between the ages of a father and mother is 4 years. If their present ages are in the ratio 9:8, find their current ages.
11. A man’s age is three times the age of his son. Five years ago, the ratio of their ages was 4:1. Find their present ages.
12. A mother and daughter’s ages add up to 50 years. If the mother is 4 times as old as her daughter, find their current ages.
13. The sum of the ages of a grandfather, father, and son is 120 years. If the father is twice the age of the son and the grandfather is twice the age of the father, find their present ages.
14. A father is twice as old as his son, and 10 years ago he was 3 times as old. Find their present ages.
15. The ratio of ages of a man and his wife is 5:4. If the man is 45 years old, find the age of his wife.
16. A father and his son’s ages add up to 70 years. If 5 years ago the father was 8 times as old as the son, find their ages.
17. The sum of the ages of a mother, father, and their child is 96 years. If the father is 4 times as old as the child, and the mother is 3 times as old as the child, find their present ages.
18. A sister is 4 years older than her brother. In 6 years, her age will be 1.5 times her brother’s age. Find their current ages.
19. The age difference between a father and son is 26 years. After 4 years, the father’s age will be 3 times his son’s age. Find their present ages.
20. A man is 25 years older than his son. After 5 years, the ratio of their ages will be 6:1. Find their present ages.

Type 2: Three Person Age Problems

1. The sum of ages of A, B, and C is 75 years. If A is twice as old as B and B is 5 years older than C, find their present ages.
2. The average age of three friends is 25 years. If the age of the youngest is 20, find the difference between the oldest and the middle friend if their difference is 10 years.
3. The ratio of ages of P, Q, and R is 2:3:5. If the sum of their ages is 100, find their present ages.
4. The sum of ages of three brothers is 84 years. If the eldest is twice the youngest, and the middle one is 4 years older than the youngest, find their ages.
5. A, B, and C have ages in the ratio 3:4:7. After 10 years, their ages will be in the ratio 4:5:8. Find their present ages.
6. The average age of a father, mother, and son is 30 years. If the father is 36 years old and the mother is 34, find the son’s age.
7. The sum of ages of three sisters is 60 years. If their ages are in the ratio 2:3:5, find their ages.
8. The present ages of A, B, and C are in the ratio 1:2:3. After 5 years, the sum of their ages will be 72. Find their present ages.
9. The difference between the ages of A and B is 6 years. The difference between B and C is 4 years. If the sum of their ages is 56, find their present ages.
10. The average age of three persons A, B, and C is 28 years. If A is 4 years older than B and B is 6 years older than C, find their present ages.
11. The present ages of three persons are in the ratio 4:7:9. If the sum of their ages is 120 years, find their ages.
12. The ratio of ages of a father, mother, and son is 6:5:2. If the difference between the father’s and son’s ages is 28 years, find their present ages.
13. The sum of ages of three cousins is 54 years. Four years ago, their ages were in the ratio 2:3:4. Find their present ages.
14. The difference between the ages of X and Y is 8 years, and the difference between Y and Z is 6 years. If their total age is 72 years, find their present ages.
15. A, B, and C are 5 years apart in age. If their total age is 72, find their ages.
16. The sum of ages of three brothers is 93 years. If their ages are in the ratio 2:3:4, find their present ages.
17. The present ages of A, B, and C are in the ratio 3:5:7. After 5 years, the sum of their ages will be 75. Find their present ages.
18. The sum of the ages of three children born at intervals of 4 years each is 36 years. Find their ages.
19. The present ages of three people are in the ratio 2:3:4. If the difference between the oldest and youngest is 14 years, find their present ages.
20. The average age of A, B, and C is 24 years. If the ratio of their ages is 3:4:5, find their present ages.

Category 3: Advanced Age Problems

‘Advanced Age Problems’ questions are more challenging and often involve concepts like average age, combined ages, or conditions spanning several years. They typically require multiple steps and careful analysis of how all individuals’ ages relate to each other. Look at the sample questions below for practice.

Type 1: Generational Age Problems

1. A father is 3 times as old as his son. In 15 years, he will be twice as old. Find their present ages.
2. A man’s present age is four times his son’s. Five years ago, he was seven times as old. Find their present ages.
3. The ratio of ages of a mother and daughter is 7:2. After 14 years, the ratio will be 9:5. Find their present ages.
4. A father is 28 years older than his son. After 10 years, the ratio of their ages will be 7:4. Find their present ages.
5. A mother is twice the age of her daughter. If the difference in their ages is 24 years, find their present ages.
6. A father and son’s ages add up to 56 years. Four years ago, the father was five times as old as his son. Find their present ages.
7. A grandfather is 8 times as old as his grandson. After 15 years, he will be 3 times as old. Find their present ages.
8. The ratio of the ages of a father and his son is 10:3. After 6 years, the ratio becomes 4:1. Find their present ages.
9. A man’s age is 3 times the sum of the ages of his two sons. Five years hence, his age will be double their ages together. Find their present ages.
10. A father is twice the age of his son and half the age of his father. If the grandfather is 72, find the father’s and son’s ages.
11. The average age of a father, mother, and daughter is 40 years. If the mother is 8 years younger than the father and the daughter is 25 years younger than the mother, find their ages.
12. A father’s age is 3 years more than three times his son’s. After 3 years, the father will be 10 years less than four times his son’s age. Find their present ages.
13. A grandmother is 4 times as old as her granddaughter. In 12 years, she will be twice as old. Find their present ages.
14. The ratio of ages of father and daughter is 7:3. After 6 years, the sum of their ages will be 66. Find their present ages.
15. A man’s age is 5 times his daughter’s. Five years ago, he was 9 times her age. Find their present ages.
16. The difference between the ages of a father and son is 24 years. After 6 years, the father’s age will be twice the son’s. Find their present ages.
17. A mother’s present age is twice the age of her daughter. After 12 years, she will be 10 years older than twice her daughter’s age. Find their present ages.
18. A father’s age is 5 times the age of his son. After 20 years, the ratio of their ages will be 3:2. Find their present ages.
19. A father and son are 30 years apart. After 5 years, the father will be 4 times as old as his son. Find their present ages.
20. The ratio of ages of a grandfather, father, and son is 12:6:1. If the sum of their ages is 133 years, find their present ages.

Type 2: Complex Ratio Problems

1. The present ages of A and B are in the ratio 5:3. Five years later, their ages will be in the ratio 10:7. Find their present ages.
2. The ratio of ages of two friends is 7:5. After 6 years, the ratio will be 4:3. Find their present ages.
3. The present ages of A and B are in the ratio 3:2. After 10 years, their ages will be in the ratio 7:5. Find their present ages.
4. The ratio of ages of two sisters is 8:5. After 9 years, the ratio will be 11:8. Find their present ages.
5. The present ages of two brothers are in the ratio 4:3. After 15 years, the ratio will become 7:6. Find their present ages.
6. The ratio of ages of two people is 7:4. Six years ago, the ratio was 11:6. Find their present ages.
7. A and B are in the ratio 9:7. After 6 years, the ratio becomes 15:13. Find their present ages.
8. The ages of A and B are in the ratio 5:7. Four years ago, the ratio was 3:5. Find their present ages.
9. The present ages of two people are in the ratio 13:11. Nine years from now, the ratio will be 17:15. Find their present ages.
10. The ratio of ages of a father and son is 7:3. After 5 years, the ratio becomes 2:1. Find their present ages.
11. The present ages of two cousins are in the ratio 11:7. Eight years later, the ratio will be 15:11. Find their present ages.
12. The ratio of ages of two sisters is 5:2. After 18 years, the ratio will be 8:5. Find their present ages.
13. The ages of A and B are in the ratio 19:17. Four years later, the ratio will be 11:10. Find their present ages.
14. The ratio of ages of two brothers is 14:9. After 7 years, the ratio will be 19:13. Find their present ages.
15. The present ages of A and B are in the ratio 10:7. Five years ago, the ratio was 13:9. Find their present ages.
16. The ratio of ages of two persons is 6:5. Ten years hence, the ratio will be 8:7. Find their present ages.
17. The present ages of A and B are in the ratio 9:5. Five years ago, the ratio was 2:1. Find their present ages.
18. The ratio of ages of two brothers is 15:11. After 7 years, the ratio will be 17:13. Find their present ages.
19. The present ages of A and B are in the ratio 5:4. After 5 years, the ratio becomes 6:5. Find their present ages.
20. The ratio of ages of two sisters is 3:2. Six years ago, the ratio was 5:3. Find their present ages.

Category 4: Special Age Problems

‘Special Age Problems’ type problems includes unusual or unique conditions, such as ages being perfect squares, cubes, or specific multiples. These problems encourage creative thinking and go beyond standard formula-based approaches. Examples of this type are aligned below.

Type 1: Average Age with Joining or Leaving

1. The average age of 5 family members is 30 years. If a new member joins, the average becomes 28 years. Find the age of the new member.
2. The average age of 8 persons increases by 2 years when a new person joins. If the total age of the original 8 persons is 240 years, find the age of the new person.
3. The average age of 6 teachers is 40 years. One teacher retires at 58 years, and a new teacher replaces him. If the average becomes 39, find the age of the new teacher.
4. The average age of 12 players is 25 years. A new player joins and the average age increases by 1 year. Find the age of the new player.
5. The average age of 10 students is 16 years. One student leaves, and the average drops by 1.5 years. Find the age of the student who left.
6. The average age of a family of 6 members is 32 years. A child of age 4 years is born. Find the new average age of the family.
7. The average age of 15 persons is 20 years. A new person joins, making the average 21. Find the age of the new person.
8. The average age of 9 cricketers is 28 years. If the captain’s age is included, the average increases by 1. Find the captain’s age.
9. The average age of 7 people decreases by 3 years when one of them leaves. If the total age of the remaining 6 people is 138, find the age of the person who left.
10. The average age of 5 members of a family is 22 years. If the age of the father is added, the average becomes 27 years. Find the father’s age.
11. The average age of 40 students is 18 years. If the teacher’s age is included, the average becomes 19. Find the teacher’s age.
12. The average age of 6 players is 30 years. A new player replaces one player of age 36, and the average becomes 29. Find the age of the new player.
13. The average age of 4 men and 2 women is 36 years. If the average age of the men is 40, find the average age of the women.
14. The average age of 20 students is 15 years. If one new student joins with age 25, find the new average age.
15. The average age of 10 people is 21 years. If a new person joins with age 41, what is the new average age?
16. The average age of 5 boys is 15 years. A new boy joins, raising the average to 16 years. Find the age of the new boy.
17. The average age of 7 people is 25 years. If the eldest person of age 55 leaves, find the new average.
18. The average age of 12 persons is 30 years. A new person of age 42 joins. Find the new average.
19. The average age of 9 workers is 32 years. A new worker joins and the average increases by 2. Find the new worker’s age.
20. The average age of 50 students is 14 years. A student of age 20 joins the class. Find the new average.

Type 2: Birth Year and Current Year Problems

1. A person was born in 1995. What will be his age in 2030?
2. If a boy is 18 years old in 2025, in which year was he born?
3. A woman was born in 1988. What was her age in 2010?
4. A child will be 15 years old in 2035. In which year was the child born?
5. If a person is 25 years old in 2020, what will be his age in 2050?
6. A man was born in 1972. How old was he in 2000?
7. A girl was 10 years old in 2015. What will be her age in 2040?
8. If a person is 40 years old in 2025, in which year was he born?
9. A boy will turn 21 years in 2030. In which year was he born?
10. A woman born in 1965 will be how old in 2025?
11. If a person was 15 years old in 2010, what is his age in 2040?
12. A man will be 50 years old in 2040. In which year was he born?
13. A girl was born in 2004. How old will she be in 2070?
14. If a boy was 12 years old in 2010, in which year was he born?
15. A person born in 1980 will be how old in 2050?
16. A woman was 25 years old in 2005. What will be her age in 2035?
17. A man was 40 years old in 2010. In which year was he born?
18. A person born in 1999 will be how old in 2075?
19. If a girl was 9 years old in 2012, what will be her age in 2050?
20. A man born in 1970 will be how old in 2035?

Type 2: Percentage-Based Age Problems

1. A father’s age is 200% of his son’s age. If the son is 15, find the father’s age.
2. A man is 150% as old as his brother. If the brother is 20, find the man’s age.
3. A girl’s age is 80% of her mother’s age. If the mother is 50, find the girl’s age.
4. A boy’s age is 25% of his father’s. If the father is 48, find the boy’s age.
5. A woman’s age is 120% of her friend’s. If the friend is 30, find her age.
6. A father’s age is 250% of his son’s. If the father is 60, find the son’s age.
7. A man is 75% of his brother’s age. If the man is 27, find the brother’s age.
8. A girl’s age is 40% of her mother’s age. If the mother is 55, find the girl’s age.
9. A woman is 90% as old as her husband. If the husband is 50, find the woman’s age.
10. A boy’s age is 10% of his grandfather’s age. If the boy is 8, find the grandfather’s age.
11. A man’s age is 300% of his son’s age. If the son is 12, find the man’s age.
12. A girl’s age is 60% of her father’s age. If she is 18, find her father’s age.
13. A man’s age is 125% of his friend’s. If the friend is 24, find his age.
14. A father is 350% of his son’s age. If the father is 70, find the son’s age.
15. A brother’s age is 110% of his sister’s. If the sister is 20, find the brother’s age.
16. A girl’s age is 15% of her mother’s. If the mother is 40, find the girl’s age.
17. A father’s age is 400% of his son’s. If the son is 10, find the father’s age.
18. A man’s age is 180% of his wife’s. If the wife is 25, find the man’s age.
19. A woman’s age is 95% of her husband’s. If the woman is 38, find the husband’s age.
20. A girl’s age is 20% of her grandmother’s. If the grandmother is 75, find the girl’s age.

Category 5: Trick Questions and Word Problems

Trick questions are designed to test attention to detail. They may appear long or complicated, but breaking them down into smaller parts often reveals a simple solution. Practising these helps improve accuracy and speed. Find sample questions of this type below.

Type 1: Age Puzzle Problems

1. The sum of A’s and B’s ages is 50 years. Ten years ago, A was twice as old as B. Find their present ages.
2. The difference between the ages of a father and his son is 30 years. Five years ago, the father was 7 times as old as the son. Find their ages.
3. The present age of a mother is three times her daughter’s age. After 12 years, the mother will be twice as old as the daughter. Find their present ages.
4. A is 4 years older than B. The ratio of their ages 4 years ago was 5:4. Find their present ages.
5. Ten years ago, the average age of a father and son was 20 years. Now the father’s age is twice the son’s. Find their current ages.
6. The sum of the ages of a man and his son is 60 years. Six years ago, the man’s age was five times that of his son. Find their present ages.
7. The present age of a father is 5 times his son’s age. After 20 years, the father will be just twice as old as his son. Find their present ages.
8. A is 2 years younger than B. After 6 years, the ratio of their ages will be 12:13. Find their present ages.
9. The present age of a brother is twice his sister’s age. Four years later, the ratio of their ages will be 13:8. Find their present ages.
10. The present age of a father is 8 times that of his son. After 15 years, the father will be twice as old as the son. Find their present ages.
11. Five years ago, the ratio of the ages of A and B was 2:3. After 10 years, their ratio will be 4:5. Find their present ages.
12. The present age of a mother is 4 times her son’s age. After 20 years, she will be only twice as old as her son. Find their present ages.
13. The sum of the ages of three brothers is 72 years. The youngest is half the age of the eldest. If the middle one is 6 years older than the youngest, find their present ages.
14. Ten years ago, a father was 7 times his son’s age. Ten years later, he will be only twice his son’s age. Find their present ages.
15. The difference between the ages of a man and his wife is 6 years. Six years ago, the man’s age was four times the age of his son. If the wife is now twice the son’s age, find the ages of all three.
16. The sum of the present ages of A, B, and C is 81 years. Five years ago, their ages were in the ratio 1:2:3. Find their present ages.
17. The present age of a father is 3 times the age of his son. Fifteen years later, the father will be twice the son’s age. Find their present ages.
18. The sum of the ages of two sisters is 44 years. Four years ago, the elder was twice the younger. Find their present ages.
19. The present age of A is 3 years more than twice the age of B. After 5 years, the sum of their ages will be 45 years. Find their present ages.
20. Four years ago, the ratio of the ages of P and Q was 5:7. After 6 years, their ratio will become 3:4. Find their present ages.

Explore: Maths Teacher Interview Questions with Sample Answers

Best Books for Quantitative Reasoning: Problems on Ages

For students preparing for competitive exams, referring to the right books can make a significant difference in mastering age-related problems. The following books are highly recommended for practising problems on ages and enhancing quantitative reasoning skills:

• Quantitative Aptitude by R.S. 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

Tricks and Tips for Solving Problems on Ages

Candidates who are unfamiliar with age-related problems may often skip these questions or make errors while attempting them. The following tips can help you tackle such problems systematically and improve accuracy:

1. Pay close attention to all the details and conditions provided in the question before attempting to solve it.
2. Start by assigning variables to unknown ages and gradually translate the word problem into a clear equation.
3. Most age problems can be solved using simple addition, subtraction, multiplication, or division. No advanced calculations are required.
4. Properly: Ensure all given information is correctly represented in the equation to avoid mistakes.
5. Once the equation is set, solve it carefully to find the correct ages.
6. Always double-check your solution by substituting the values back into the original equation to confirm accuracy.

Problems on ages are an essential part of quantitative aptitude in competitive exams. While they may appear tricky at first, understanding the basic concepts, formulas, and different types of questions makes them manageable and highly scoring.

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