50+ Problems on Ages Questions and Answers (Concept, Tricks & Solutions for SSC, Bank Exams)

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Problems on Ages quiz

Problems on Ages – Concept and Basics

Problems on Ages are one of the most common topics in aptitude sections of competitive exams like SSC, Bank, Railway, GRE, and campus placements.

These questions test your ability to understand relationships between present, past, and future ages.

If you know the basic formulas and shortcuts, you can solve these questions in just a few seconds.

In this article, you will learn:

  • Problems on Ages concept
  • Important formulas
  • Quick tricks
  • Solved examples
  • Practice questions
Problems on Ages Practice Tests
Problems on Ages Quiz 1 Problems on Ages Quiz 2 Problems on Ages Quiz 3(Inactive)

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Tricks to Solve Problems on Ages Quickly

Trick 1: Age Difference Never Changes

The difference between the ages of two people always remains constant.

Example:

Father = 50
Son = 20

Difference = 30 years

After 10 years:

Father = 60
Son = 30

Difference = 30 years

Trick 2: Use Variables

If age is unknown, assume a variable.

Example:

Let son’s age = x

Father’s age = x + 25

Trick 3: Convert Ratios to Actual Ages

If age ratio is given:

Father : Son = 5 : 2

Let ages be:

5x and 2x

Important formulas

Given below are a few formulas connected to the problems on ages that may help you answer the questions faster and acquire a better understanding of the concept:

  • If you assume that the current age is x, the age after n years will be (x+n) years.
  • If you assume that the current age is x, the age before n years is (x-n) years.
  • If the age is given in the form of a ratio, for example, p:q, the age will be treated as qx and px.
  • Assuming a current age of x, multiplying by n yields (x×n) years
  • If you assume the present age is x, then 1/n of the age must be equal to (x/n) years.

Sample Questions: Age-related Problems

Q 1. What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.

a. 6.2 years
b. 7.7 years
c. 8.7 years
d. 10 years

Correct Option: (c)
Solution:
1) Let John’s present age be x
2) John’s age before 5 years = (x – 5)
3) John’s age after 10 years = (x + 10)
We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)
Therefore,
(x + 10) = 5 (x – 5)
Solving the equation, we get
x + 10 = 5x – 25
4x = 35
x = 8.75 years

Q2. A father said his son, ” I was as old as you are at present at the time of your birth. ” If the father age is 38 now, the son age 5 years back was :

a. 14

b. 19

c. 33

d. 38

Correct Option: (a) 14
Solution:
Let the son’s present age be x years. Then, (38 – x) = x => x= 19. 

Son’s age 5 years back = (19 – 5) = 14 years

Q3. The ratio of the Mother’s age to her daughter’s age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :

  1. 1 : 3
  2. 2 : 3
  3. 3 : 4
  4. 5 : 3

Correct Option: (D) 5:3

Solution:

Let the present ages of the Mother and daughter be 9x and 5x respectively.

9x × 5x = 1125   ⇒   45x2 = 1125  ⇒  x2 = 25  ⇒  x = 5.
Required ratio  = (9x + 5) : (5x + 5)  ⇒   50 : 30  ⇒  5 : 3.  

Hence, option D is correct.

Q4. Raj’s age is 4 times that of Dhiraj, his cousin. 3 years back, Raj was 5 times as old as Dhiraj. What is his present age?

a. 12 years
b. 16 years
c. 24 years
d. 48 years

Correct Option: (D). 48 years
Solution:
Present day,
Let us consider Dhiraj’s present age as K years
Raj’s present age is 4 times Dhiraj’s = 4K years
3 years ago,
Dhiraj’s age = K-3 years
Raj’s age = 4K-3 years.
That time, Raj’s age = 5 times Dhiraj’s age
∴ 4K-3 = 5(K-3)
4K-3 = 5K-15
∴ K = 12 years

Present age of Raj = 4K = 4 x 12 = 48 years.

Q5. Rahul is 15 years elder than Rohan. If 5 years ago, Rahul was 3 times as old as Rohan, then find Rahul’s present age.

a. 32.5 years
b. 27.5 years
c. 25 years
d. 24.9 years

Correct Option: (B) 27.5 years

Solution:
1) Let age of Rohan be y
2) Rahul is 15 years elder than Rohan = (y + 15). So Rahul’s age 5 years ago = (y + 15 – 5)
3) Rohan’s age before 5 years = (y – 5)
5 years ago, Rahul is 3 times as old as Rohan
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25
y = 12.5
Rohan’s age = 12.5 years
Rahul’s age = (y + 15) = (12.5 + 15) = 27.5 years

Q6.The present ages of three colleague’s are in proportions 3 : 5 : 7. Four years ago, the sum of their ages was 48. find their present ages (in years) ?

  1. 12 , 20 and 28 years
  2. 13 , 15  and 23 years
  3. 11 , 16 and 19 years
  4. 20,  24 and 27 years
  5. None of these

Correct Option: (A) 12 , 20 and 28 years

Solution:

Let the present age of three colleague’s are :   3x, 5x and 7x
(3x – 4) + (5x – 4) + (7x – 4) = 48.
15x – 12 = 48 ⇒ 15x = 60 ⇒ x = 4.
Their present ages are 12 years, 20 years and 28 years respectively.

Hence, option A is correct.

Q7. A, B and C’s age are such that A is youngest and C is eldest. Also the difference between A and B’s age is same as the difference between B and C’s age. The sum of A and C’s age is 108. Find B’s age.

a. 32 years
b. 36 years
c. 54 years
d. 64 years

Correct Option: c. 54 years
Solution:

A’s age < B’s age < C’s age

Difference in A’s and B’s age = Difference in B’s and C’s age

This means that B’s age is at the middle of A’s and C’s ages.

B’s Age = (Sum of A’s and C’s ages)/2 =108/2= 54years.

Q 8. Age of mother 10 years ago was 3 times the age of her son. After 10 years, mother’s age will be twice that of his son. Find the ratio of their present ages.

a. 11 : 7
b. 9 : 5
c. 7 : 4
d. 7 : 3

Correct Option: (D) 7:3

Solution:

We are given that, age of mother 10 years ago was 3 times the age of her son
So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.
At present: Mother’s age will be (3x + 10) and son’s age will be (x + 10)
After 10 years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10
Mother’s age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3

Problems on Ages for Competitive Exams

Age problems frequently appear in exams such as:

  • SSC CGL
  • SSC CHSL
  • Bank PO
  • Bank Clerk
  • Railway Exams
  • Campus Placement Tests

Practicing these questions regularly improves your speed and accuracy.

Tips to Solve Age Problems Faster

Follow these tips during exams:

  • Always assume variables for unknown ages
  • Remember age difference remains constant
  • Convert ratios into equations
  • Use elimination when possible
  • Practice regularly

With practice, you can solve most age questions in less than 30 seconds.

Problems on Ages are simple if you understand the basic concepts and formulas. These questions appear frequently in SSC, Bank, Railway, and other competitive exams.

By learning the tricks and practicing solved examples, you can solve age problems quickly and improve your aptitude score.

Make sure to practice multiple questions and review shortcuts regularly.