We have already covered Age Concepts and Age Formulas. Now it is time to apply those concepts and formulas to different types of Age Problems and learn how to solve them step by step.
In this chapter, we will solve Age Problems of different types and difficulty levels, understand how to identify the information given in a question, apply the appropriate age concept or formula, and arrive at the correct answer.
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So, let us start solving Age Problems.
Question 1: Apsara is 4 years older than her brother. Three years ago, the sum of their ages was 36 years. What is Apsara’s present age?
Solution
Given:
- Apsara is 4 years older than her brother.
- Three years ago, the sum of their ages was 36 years.
Let the present age of Apsara’s brother be x years.
Apsara’s present age = x + 4 years
Formula / Concept We Can Use:
Age N Years Ago = Present Age − N
Three years ago:
Brother’s age = x − 3
Apsara’s age = x + 4 − 3 = x + 1
According to the question:
x − 3 + x + 1 = 36
2x − 2 = 36
2x = 38
x = 19
Therefore, Apsara’s present age:
19 + 4 = 23 years
Answer: 23 years
Question 2: Apsara is 5 years younger than her brother. After 4 years, her brother will be 29 years old. What was Apsara’s age 3 years ago?
Solution
Given:
- Apsara is 5 years younger than her brother.
- After 4 years, her brother will be 29 years old.
Let the present age of Apsara’s brother be x years.
Apsara’s present age = x − 5 years
Formula / Concept We Can Use:
Age N Years From Now = Present Age + N
After 4 years, brother’s age will be 29:
x + 4 = 29
x = 25
Therefore, Apsara’s present age:
25 − 5 = 20 years
Apsara’s age 3 years ago:
20 − 3 = 17 years
Answer: 17 years
Question 3: Apsara’s present age is 4 years more than twice her brother’s age. If her brother is 11 years old, what will be Apsara’s age 6 years from now?
Solution
Given:
- Apsara’s present age is 4 years more than twice her brother’s age.
- Her brother is 11 years old.
Formula / Concept We Can Use:
Apsara’s Age = 2 × Brother’s Age + 4
Apsara’s present age:
2 × 11 + 4 = 26 years
After 6 years:
26 + 6 = 32 years
Answer: 32 years
Question 4: The present ages of Apsara and her brother differ by 7 years. Four years ago, Apsara was twice as old as her brother. What is Apsara’s present age?
Solution
Given:
- Apsara and her brother have an age difference of 7 years.
- Four years ago, Apsara was twice as old as her brother.
Let the present age of Apsara’s brother be x years.
Apsara’s present age = x + 7 years
Formula / Concept We Can Use:
Age N Years Ago = Present Age − N
Four years ago:
Brother’s age = x − 4
Apsara’s age = x + 7 − 4 = x + 3
According to the question:
x + 3 = 2(x − 4)
x + 3 = 2x − 8
x = 11
Therefore, Apsara’s present age:
11 + 7 = 18 years
Answer: 18 years
Question 5: The present ages of Apsara and her brother are in the ratio 5 : 7. After 6 years, the sum of their ages will be 60 years. What is Apsara’s present age?
Solution
Given:
- Present age ratio of Apsara and her brother = 5 : 7
- Sum of their ages after 6 years = 60 years
Let their present ages be 5x and 7x.
After 6 years:
5x + 6 + 7x + 6 = 60
12x + 12 = 60
12x = 48
x = 4
Apsara’s present age = 5 × 4 = 20 years
Answer: 20 years
Question 6:The present ages of Apsara and her brother are in the ratio 4 : 7. If the sum of their present ages is 55 years, what is Apsara’s present age?
Solution
Given:
- Present age ratio of Apsara and her brother = 4 : 7
- Sum of their present ages = 55 years
Let their present ages be 4x and 7x.
4x + 7x = 55
11x = 55
x = 5
Apsara’s present age = 4 × 5 = 20 years
Answer: 20 years
Question 7: The present ages of two RRB NTPC aspirants are in the ratio 5 : 7. After 6 years, the ratio of their ages will become 11 : 15. What is the present age of the younger aspirant?
Solution
Given:
- Present age ratio of the two RRB NTPC aspirants = 5 : 7
- After 6 years, their age ratio = 11 : 15
Let their present ages be 5x and 7x.
After 6 years:
(5x + 6) / (7x + 6) = 11 / 15
15(5x + 6) = 11(7x + 6)
75x + 90 = 77x + 66
24 = 2x
x = 12
Present age of the younger aspirant = 5 × 12 = 60 years
Answer: 60 years
Question 8: The average age of 6 RRB employees is 28 years. When their manager’s age is included, the average age becomes 30 years. What is the manager’s age?
Solution
Given:
- Average age of 6 RRB employees = 28 years
- Average age of 7 people including the manager = 30 years
Formula / Concept We Can Use:
Total Age = Average Age × Number of People
Total age of 6 employees:
28 × 6 = 168 years
Total age including the manager:
30 × 7 = 210 years
Manager’s age:
210 − 168 = 42 years
Answer: 42 years
Question 9: A father is 3 times as old as his son. Eight years ago, the father was 5 times as old as his son. What is the present age of the son?
Solution
Given:
- Father’s present age = 3 times the son’s present age.
- Eight years ago, father’s age was 5 times the son’s age.
Let the present age of the son be x years.
Father’s present age = 3x years
Formula / Concept We Can Use:
Age N Years Ago = Present Age − N
Solution:
Eight years ago:
Son’s age = x − 8
Father’s age = 3x − 8
According to the question:
3x − 8 = 5(x − 8)
3x − 8 = 5x − 40
32 = 2x
x = 16
Therefore, the son’s present age = 16 years
Answer: 16 years
Question 10: In a government department, an ASO is 6 years older than his immediate junior. If twice the junior’s age is 8 years more than the ASO’s age, what is the ASO’s present age?
Solution
Given:
- ASO is 6 years older than his immediate junior.
- Twice the junior’s age is 8 years more than the ASO’s age.
Let the present age of the junior be x years.
ASO’s present age = x + 6 years
Formula / Concept We Can Use:
Age-based equation: More than → Add
According to the question:
2x = x + 6 + 8
2x = x + 14
x = 14
Therefore, ASO’s present age:
14 + 6 = 20 years
Answer: 20 years
Question 11: At a railway station, the Station Master is 4 years older than his immediate junior. The junior is 6 years older than another employee. If the sum of the ages of all three employees is 79 years, what is the present age of the Station Master?
Solution
Given:
- Station Master’s age is 4 years more than his immediate junior.
- The junior is 6 years older than another employee.
- Sum of the ages of all three employees = 79 years.
Let the age of the other employee be x years.
Junior’s age = x + 6 years
Station Master’s age = x + 6 + 4 = x + 10 years
x + (x + 6) + (x + 10) = 79
3x + 16 = 79
3x = 63
x = 21
Therefore, Station Master’s present age:
21 + 10 = 31 years
Answer: 31 years
Question 12: The present ages of Apsara and her brother are in the ratio 5 : 7. Six years ago, their ages were in the ratio 2 : 3. What will be the ratio of their ages 5 years from now?
Solution
Given:
- Present age ratio of Apsara and her brother = 5 : 7
- Six years ago, their age ratio = 2 : 3
Let their present ages be 5x and 7x.
Six years ago:
(5x − 6) / (7x − 6) = 2 / 3
3(5x − 6) = 2(7x − 6)
15x − 18 = 14x − 12
x = 6
Present ages:
Apsara = 5 × 6 = 30 years
Brother = 7 × 6 = 42 years
After 5 years:
Apsara = 35 years
Brother = 47 years
Ratio = 35 : 47
Answer: 35 : 47
Question 13: Apsara is 8 years older than her brother. Her sister is 5 years younger than Apsara. Six years ago, the sister was twice as old as the brother was at that time. What is Apsara’s present age?
Solution
Given:
- Apsara is 8 years older than her brother.
- Apsara’s sister is 5 years younger than Apsara.
- Six years ago, the sister was twice as old as the brother.
Let the present age of Apsara’s brother be x years.
Apsara’s present age = x + 8 years
Sister’s present age = x + 8 − 5 = x + 3 years
Formula / Concept We Can Use:
Age N Years Ago = Present Age − N
Solution:
Six years ago:
Brother’s age = x − 6
Sister’s age = x + 3 − 6 = x − 3
According to the question:
x − 3 = 2(x − 6)
x − 3 = 2x − 12
x = 9
Therefore, Apsara’s present age:
9 + 8 = 17 years
Answer: 17 years
Question 14: The present ages of three RRB NTPC aspirants A, B and C are such that A : B = 2 : 3 and B : C = 4 : 5. After 5 years, the ratio of A’s age to C’s age will be 3 : 5. What is C’s present age?
Solution
Given:
- A : B = 2 : 3
- B : C = 4 : 5
- After 5 years, A : C = 3 : 5
Make B common in both ratios:
A : B = 8 : 12
B : C = 12 : 15
Therefore, present ages are:
A = 8x
B = 12x
C = 15x
Formula / Concept We Can Use:
For ages after N years:
Age after N years = Present Age + N
Solution:
After 5 years:
A = 8x + 5
C = 15x + 5
According to the question:
(8x + 5) / (15x + 5) = 3 / 5
5(8x + 5) = 3(15x + 5)
40x + 25 = 45x + 15
10 = 5x
x = 2
Therefore, C’s present age:
15 × 2 = 30 years
Answer: 30 years
Question 15: The average age of three railway employees A, B and C is 22 years. The present ages of A and B are in the ratio 2 : 3. B is 6 years older than C. What is C’s present age?
Solution
Given:
- Average age of A, B and C = 22 years
- A : B = 2 : 3
- B is 6 years older than C
Let the present ages of A and B be 2x and 3x.
C’s age = 3x − 6 years
Formula / Concept We Can Use:
Total Age = Average Age × Number of People
Solution:
Total age of A, B and C:
22 × 3 = 66 years
Therefore:
2x + 3x + (3x − 6) = 66
8x − 6 = 66
8x = 72
x = 9
C’s present age:
3 × 9 − 6 = 21 years
Answer: 21 years
Question 16: Sankirtan is 4 years older than twice his brother’s age. His brother is 20 years younger than their father. If the sum of their ages is 64 years, what is the present age of the father?
Solution
Given:
- Sankirtan is 4 years older than twice his brother’s age.
- His brother is 20 years younger than their father.
- Sum of their ages = 64 years.
Let the present age of Sankirtan’s brother be x years.
Sankirtan’s age = 2x + 4 years
Father’s age = x + 20 years
Formula / Concept We Can Use:
Age-based equation: More than → Add
Solution:
According to the question:
x + (2x + 4) + (x + 20) = 64
4x + 24 = 64
4x = 40
x = 10
Father’s present age:
10 + 20 = 30 years
Answer: 30 years
What We Learned in Age Questions
In these competitive-exam level questions, we learned how to:
- Solve problems using age difference and sum.
- Calculate past and future ages.
- Solve age-ratio and changing-ratio problems.
- Apply average age concepts.
- Solve parent-child and family age problems.
- Convert age relationships into mathematical equations.
- Handle multiple people and multiple age conditions.
- Combine different concepts to solve mixed and difficult Age Problems.
These questions show how Age Problems are asked in competitive examinations, where more than one condition may need to be applied to reach the answer.