Problem on Ages
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Solved Examples
Study MaterialSolved Examples – Problem on Ages
Solved examples help students understand the practical application of Problems on Ages in competitive examinations. These examples are designed from basic to advanced level and cover important concepts frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Present Age Problems
- Past and Future Age Problems
- Ratio of Ages
- Average Age Problems
- Father-Son Age Relations
- Mother-Daughter Age Relations
- Addition and Removal of Persons
- Age Difference Concepts
- Linear Equation Method
- Logical Age-Based Puzzles
Example 1: Basic Present Age Problem
Question: A person's age is increased by 8 years to become 35 years. Find the present age.
Solution:
Let present age = x
According to question:
x + 8 = 35
x = 35 − 8
x = 27 years
Example 2: Future Age Problem
Question: The present age of Ravi is 18 years. What will be his age after 7 years?
Solution:
Future age:
= 18 + 7
= 25 years
Example 3: Past Age Problem
Question: The present age of Sita is 32 years. What was her age 9 years ago?
Solution:
Past age:
= 32 − 9
= 23 years
Example 4: Father and Son Age Problem
Question: A father is 4 times as old as his son. If the son's age is 12 years, find the father's age.
Solution:
Son's age = 12 years
Father's age:
= 4 × 12
= 48 years
Example 5: Ratio of Ages
Question: The ages of two persons are in the ratio 3 : 5. If their total age is 64 years, find their ages.
Solution:
Let ages be:
3x and 5x
According to question:
3x + 5x = 64
8x = 64
x = 8
Required ages:
3x = 24 years
5x = 40 years
Therefore:
24 years and 40 years
Example 6: Age Difference Problem
Question: The present ages of two brothers are 18 years and 25 years. Find the difference between their ages after 15 years.
Solution:
Present difference:
25 − 18 = 7 years
Difference between ages never changes.
Therefore:
Difference after 15 years = 7 years
Example 7: Future Ratio Problem
Question: The present ages of A and B are in the ratio 2 : 3. After 6 years, their ages will be in the ratio 3 : 4. Find their present ages.
Solution:
Let present ages be:
2x and 3x
According to question:
(2x + 6)/(3x + 6) = 3/4
4(2x + 6) = 3(3x + 6)
8x + 24 = 9x + 18
x = 6
Present ages:
2x = 12 years
3x = 18 years
Therefore:
12 years and 18 years
Example 8: Past Ratio Problem
Question: The present ages of two persons are 30 years and 40 years. What was the ratio of their ages 5 years ago?
Solution:
5 years ago:
30 − 5 = 25
40 − 5 = 35
Ratio:
25 : 35
= 5 : 7
Therefore:
5 : 7
Example 9: Average Age Problem
Question: The average age of 6 students is 14 years. Find their total age.
Solution:
Total age:
= Average × Number of persons
= 14 × 6
= 84 years
Example 10: Addition of a Person
Question: The average age of 8 persons is 25 years. A new person joins the group and the average becomes 26 years. Find the age of the new person.
Solution:
Old total age:
= 8 × 25
= 200
New total age:
= 9 × 26
= 234
Age of new person:
= 234 − 200
= 34 years
Example 11: Removal of a Person
Question: The average age of 10 persons is 32 years. One person leaves and the average becomes 30 years. Find the age of the person who left.
Solution:
Original total age:
= 10 × 32
= 320
New total age:
= 9 × 30
= 270
Age of removed person:
= 320 − 270
= 50 years
Example 12: Mother and Daughter Age Problem
Question: A mother is 3 times as old as her daughter. If the daughter's age is 15 years, find the mother's age.
Solution:
Mother's age:
= 3 × 15
= 45 years
Example 13: Linear Equation Method
Question: Five years ago, a person's age was 20 years. Find the present age.
Solution:
Let present age = x
According to question:
x − 5 = 20
x = 25
Present age = 25 years
Example 14: Twice Older Statement
Question: A father is twice older than his son. If the son's age is 10 years, find the father's age.
Solution:
"Twice older" means:
Son's age + 2 × Son's age
= 3 × Son's age
Father's age:
= 3 × 10
= 30 years
Example 15: Combined Average Age
Question: The average age of 5 boys is 12 years and the average age of 7 girls is 14 years. Find the average age of the entire group.
Solution:
Total age of boys:
= 5 × 12
= 60
Total age of girls:
= 7 × 14
= 98
Combined average:
= (60 + 98)/(5 + 7)
= 158/12
= 13.17 years
Example 16: Age Relation Puzzle
Question: Ten years ago, the ratio of ages of A and B was 3 : 5. Their present ages are in the ratio 5 : 7. Find their present ages.
Solution:
Let present ages be:
5x and 7x
Ten years ago:
(5x − 10)/(7x − 10) = 3/5
5(5x − 10) = 3(7x − 10)
25x − 50 = 21x − 30
4x = 20
x = 5
Present ages:
25 years and 35 years
Example 17: Difference-Based Shortcut
Question: The ratio of ages of two persons is 4 : 7 and their age difference is 18 years. Find their ages.
Solution:
Difference in ratio:
7 − 4 = 3
3x = 18
x = 6
Ages:
4x = 24 years
7x = 42 years
Therefore:
24 years and 42 years
Example 18: Grandfather-Father-Son Problem
Question: The ages of grandfather, father, and son are in the ratio 8 : 5 : 2. If their total age is 105 years, find their ages.
Solution:
Let ages be:
8x, 5x, and 2x
According to question:
8x + 5x + 2x = 105
15x = 105
x = 7
Required ages:
Grandfather = 56 years
Father = 35 years
Son = 14 years
Important Exam Tips
- Always assume present age as x whenever possible.
- Use only one variable to simplify equations.
- Remember that age difference never changes.
- Read ratio statements carefully.
- Avoid confusion between "times older" and "times as old".
- Use cross multiplication correctly in ratio problems.
- Verify equations before solving.
Practicing solved examples regularly improves logical reasoning, equation formation skills, and accuracy in solving Problems on Ages in competitive examinations.