We have covered Age Concepts, Age Formulas, Age Questions with Answers & Solutions, and Age Practice Questions. Now it is time to practice previous-year questions (PYQs) asked in SSC, RRB, Defence, Police, Banking and other competitive examinations.
The questions are provided with solutions, but aspirants are advised to attempt each question themselves before checking the solution. This will help you improve your calculation skills, understand how Age Problems are asked in actual examinations, and strengthen your preparation.
Note: To make the practice more engaging and useful, some PYQs may have their numbers, names or situations/context modified. The underlying concept and question pattern are retained so that you can practice the type of problem asked in competitive examinations.
So, let us start practicing Age PYQs.
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Question 1: A railway employee’s present age is one-third of the present age of his fellow employee. After 6 years, his age will be one-half of his fellow employee’s age. How old is the fellow employee at present?
Solution
Given:
- Present age of the railway employee = one-third of his fellow employee’s age.
- After 6 years, his age will be half of his fellow employee’s age.
Concept/Formula:
Let the present age of the railway employee be x years.
Then, a fellow employee’s present age = 3x years.
After 6 years:
Railway employee’s age = x + 6
Fellow employee’s age = 3x + 6
According to the question:
x + 6 = (3x + 6)/2
2x + 12 = 3x + 6
x = 6
Fellow employee’s present age:
3 × 6 = 18 years
Answer
The present age of the fellow employee is 18 years.
Question 2: A Senior Railway employee is three times as old as his junior colleague. After 12 years, the senior employee will be twice as old as the junior colleague. What is the present age of the junior colleague?
Solution
Given:
- Senior Railway employee’s present age = 3 times the junior colleague’s age.
- After 12 years, the senior employee will be twice the junior colleague’s age.
Concept/Formula:
Let the present age of the junior colleague be x years.
Then, the senior employee’s present age = 3x years.
After 12 years:
Junior colleague’s age = x + 12
Senior employee’s age = 3x + 12
According to the question:
3x + 12 = 2(x + 12)
3x + 12 = 2x + 24
x = 12
Answer
The present age of the junior colleague is 12 years.
Question 3: The ages of an SSC CGL candidate and his father are currently in the ratio 3 : 7. Four years from now, the ratio of their ages will be 2 : 4. Find the father’s age five years ago.
Solution
Given:
- The present ages of the SSC CGL candidate and his father are in the ratio 3 : 7.
- After 4 years, their ages will be in the ratio 2 : 4.
- We need to find the father’s age 5 years ago.
Concept/Formula:
Let their present ages be 3x and 7x.
After 4 years:
Candidate’s age = 3x + 4
Father’s age = 7x + 4
According to the question:
(3x + 4)/(7x + 4) = 2/4
4(3x + 4) = 2(7x + 4)
12x + 16 = 14x + 8
2x = 8
x = 4
Father’s present age:
7 × 4 = 28 years
Father’s age 5 years ago:
28 − 5 = 23 years
Answer
The father’s age five years ago was 23 years.
Question 4: A railway supervisor is currently twice as old as his junior colleague. Six years from now, their ages will be in the ratio 23 : 13. What is the supervisor’s present age?
Solution
Given:
- Present age of the railway supervisor = twice the age of his junior colleague.
- After 6 years, their ages will be in the ratio 23 : 13.
Concept/Formula:
Let the present age of the junior colleague be x years.
Then, the supervisor’s present age = 2x years.
After 6 years:
Junior colleague’s age = x + 6
Supervisor’s age = 2x + 6
According to the question:
(2x + 6)/(x + 6) = 23/13
13(2x + 6) = 23(x + 6)
26x + 78 = 23x + 138
3x = 60
x = 20
Supervisor’s present age:
2 × 20 = 40 years
Answer
The railway supervisor’s present age is 40 years.
Question 5: Three railway vendors at Kanpur railway station have ages related as follows: the first vendor is three-fifths as old as the second vendor, while the third vendor is two-thirds as old as the first vendor. The second vendor is three-fifths as old as a senior railway vendor. If the senior vendor is 75 years old, what is the present age of the third vendor?
Solution
Given:
- The first vendor is three-fifths as old as the second vendor.
- The third vendor is two-thirds as old as the first vendor.
- The second vendor is three-fifths as old as the senior railway vendor.
- Senior railway vendor’s age = 75 years.
Concept/Formula:
Use the given age ratios successively to find the ages of the vendors.
Solution:
Senior railway vendor’s age = 75 years
Second vendor’s age:
= 3/5 × 75
= 45 years
First vendor’s age:
= 3/5 × 45
= 27 years
Third vendor’s age:
= 2/3 × 27
= 18 years
Answer
The present age of the third vendor is 18 years.
Question 6: The sum of the present ages of Apsara and Sankirtan is 51 years. Six years ago, the product of their ages was 270. What is Apsara’s present age if she is older than Sankirtan?
Solution
Given:
Sum of present ages = 51 years
Six years ago, product of ages = 270
Concept/Formula:
Six years ago, sum of ages = 51 − 12 = 39 years
The two ages are 30 years and 9 years, since:
30 + 9 = 39
30 × 9 = 270
Apsara is older, so her present age = 30 + 6 = 36 years.
Answer
Apsara’s present age is 36 years.
Question 7: A Bank PO candidate was asked about his present age. He replied that if his age 3 years from now is multiplied by 3 and three times his age 3 years ago is subtracted from it, the result will be equal to his present age. What is his present age?
Solution
Given:
Age 3 years from now =
Age 3 years ago =
Concept/Formula:
Let the present age = x years.
3(x + 3) − 3(x − 3) = x
3x + 9 − 3x + 9 = x
x = 18 years
Answer
The present age of the Bank PO candidate is 18 years.
Question 8: Twenty years ago, an Income Tax Inspector was four times as old as his junior colleague. Today, the Income Tax Inspector is twice as old as his junior colleague. What is the sum of their present ages?
Solution
Given:
20 years ago, Inspector’s age = 4 times junior’s age
Present Inspector’s age = 2 times junior’s age
Concept/Formula:
Let the junior colleague’s present age = x years.
Inspector’s present age = 2x years.
Solution:
20 years ago:
2x − 20 = 4(x − 20)
2x − 20 = 4x − 80
2x = 60
x = 30
Inspector’s present age = 2 × 30 = 60 years
Sum of present ages = 30 + 60 = 90 years.
Answer
The sum of their present ages is 90 years.
Question 9: Ten years ago, the age of an IT Inspector was three times the age of his junior colleague. Ten years from now, the IT Inspector will be twice as old as his junior colleague. What is the ratio of their present ages?
Solution
Given:
10 years ago, IT Inspector’s age = 3 times junior’s age
10 years from now, IT Inspector’s age = 2 times junior’s age
Concept/Formula:
Let the junior colleague’s present age = x years.
Let the IT Inspector’s present age = y years.
10 years ago:
y − 10 = 3(x − 10)
y = 3x − 20
10 years from now:
y + 10 = 2(x + 10)
y = 2x + 10
Therefore:
3x − 20 = 2x + 10
x = 30
IT Inspector’s present age:
y = 2(30) + 10 = 70 years
Ratio of their present ages:
70 : 30 = 7 : 3
Answer
The ratio of their present ages is 7 : 3.
Question 10: Sixteen years ago, an Assistant Audit Officer (AAO) in the CAG was 5 times as old as his junior colleague. Eight years from now, the AAO will be twice as old as his junior colleague. What will be the ratio of their ages 8 years ago?
Solution
Given:
16 years ago, AAO’s age = 5 times junior colleague’s age
8 years from now, AAO’s age = 2 times junior colleague’s age
Concept/Formula:
Let the present age of the junior colleague = x years.
Let the present age of the AAO = y years.
Solution:
16 years ago:
y − 16 = 5(x − 16)
y = 5x − 64
8 years from now:
y + 8 = 2(x + 8)
y = 2x + 8
Therefore:
5x − 64 = 2x + 8
3x = 72
x = 24
AAO’s present age:
y = 2(24) + 8 = 56 years
Eight years ago:
AAO = 56 − 8 = 48 years
Junior colleague = 24 − 8 = 16 years
Ratio = 48 : 16 = 3 : 1
Answer
The ratio of their ages 8 years ago was 3 : 1.
Question 11: The combined present age of three Track Maintenance Staff in Indian Railways is 93 years. Ten years ago, their ages were in the ratio 2 : 3 : 4. What is the present age of the oldest Track Maintenance Staff?
Solution
Given:
Combined present age of three Track Maintenance Staff = 93 years
Their ages 10 years ago were in the ratio 2 : 3 : 4
Concept/Formula:
Combined age 10 years ago = 93 − (3 × 10) = 63 years
Solution:
Total ratio = 2 + 3 + 4 = 9
One part = 63 ÷ 9 = 7 years
Oldest staff’s age 10 years ago:
4 × 7 = 28 years
Present age = 28 + 10 = 38 years
Answer
The present age of the oldest Track Maintenance Staff is 38 years.