Amit Manekar

Email – amitmanekar91@gmail.com
Contact no: (+91)9096754428 / (+91)942156648

Aptitude Made Simple

Problems on Ages

Various competitive examinations ask questions regularly based on Problems on Ages.

Many students face challenges in understanding and solving problems as they are not
able to covert problem statements from words into equation of ages and ratio.

Let us take real life example and will try to understand concept of Problem of Ages.

Real life example for Problems on Ages:

Let us assume Today your age is half of your father’s age.

 If your father age is 50 years then your age would be 50/2 = 25 years
 If your father’s age is 60 years then your age would be 60/2 = 30 years
 If your father age is 100 years, your age would be 100/2 = 50 years.

Ratio of Father’s age to your age today is 2:1

Problems would be based on Today’s [Present] age, Past age or future age.
If we are able to convert problem statement into equation we have solved 80% of the
problem. We will practice initially for this before solving problem.

Assume your Present age is x years and we will understand meaning of different
statements and its respective value.

Statement Meaning in form of equation

Age after 10 years x + 10
Age after 5 years x+5
Age 10 years ago x - 10
Age 25 years ago x – 25
5 years Hence x+5
10 years Hence x + 10
Age 5 years back x–5
Age 15 years back x – 15
3 times of today’s age 3x

Assume:
Age of A : 20 Years
Age of B : 25 Years

As B’s age is more than A,

B will be referred as Elder and A will be referred as Younger

Practice these similar statements and most of the time in numbers problem, you will
either see 1 or more number of statement combination.

First step in problem would be convert problem statement into equation and then solve
it.

We will solve problems now.

Problem 1:

The ages of two persons differ by 16 years. If 6 years ago, elder one by 3 times as old
as younger one, find their present ages.

Solution :

Difference of present age for 2 Persons : 16 Years

6 Years ago, Elder age = 3 * younger age
Present ages = ?

Let us assume age of Person1 as x years

As difference between Person1 and Person2 is 16 years

Person2 age = Person1 age – 16

Person2 age = x – 16

So Person1 is elder and Person2 is Younger.

6 Years ago:
Person1 age = x - 6
Person2 age = (x – 16 ) – 6 = x - 22

It is given that 6 Years ago, Elder age = 3 * younger age

x – 6 = 3 (x – 22)
x – 6 = 3x – 66
2x = 60
x = 30

Person1 Present age = x = 30 Years

Person2 Present age = x – 16 = 30 – 16 = 14 Years.

Note: You can cross-check your answer.

Like present ages 30 and 14. So 6 years before, ages would be 24 and 8.
So elder was 3 times of younger. So our answer is correct.

Answer is Present ages of Persons are 30 Years and 14 Years

Problem 2:

The product of ages of ages of Ankit and Nikita is 240. If twice age of Nikita is more
than Ankit' s age by 4 years, what is Nikita's age?

Solution :

Age of Ankit * Age of Nikita = 240

2 * age of Nikita = Age of Ankit + 4
Nikita Age = ?

Let us assume age of Nikita is x years and age of Ankit is y years.

As it is given: 2 * age of Nikita = Age of Ankit + 4

2x = y + 4
y = 2x – 4

Age of Ankit * Age of Nikita = 240

y * x = 240
(2x – 4) x = 240
2 -4 - 240 = 0
- 2 - 120 = 0
- 12 + 10 - 120 = 0
x(x – 12) + 10(x – 12) = 0
(x + 10)(x – 12) = 0
So x + 10 = 0 or x – 12 = 0
x = -10 or x = 12
we need to ignore -10 and consider x = 12

Nikita present age = 12 years

Answer is Nikita’s age is 12 Years

Problem 3:

Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old
as his son. What are their present ages?

Solution :

8 Years ago : Rohit’s age = 4 * Son’s age

After 8 year: Rohit’s age = 2 * Son’s age

Let us assume Present age of Rohit as x years and present age of his son y years

8 Years ago:

Rohit’s age = x + 8 years

Son’s age = y + 8

Looking at given : 8 Years ago : Rohit’s age = 4 * Son’s age

x – 8 = 4 * (y – 8)

x – 8 = 4y – 32

x – 4y = - 24 --------------------------------------Equation1

After 8 Years:

Rohit’s age = x + 8 years

Son’s age = y + 8

Looking at given : After 8 year: Rohit’s age = 2 * Son’s age

x + 8 = 2 * (y + 8)

x + 8 = 2y + 16

x – 2y = 8 ------------------------------------------Equation2

x – 4y = - 24 -------------- Equation1

- x – 2y = 8 ---------------Equation2

- + -

------------------------------------------------------------
-2y = -32
-2y = -32
y = 16 [Present age of Son]

Put value of y in Equation1

x – 4y = - 24
x – (4 * 16) = -24
x – 64 = -24
x = 40 [Present age of Rohit].

Answer is Present age of Rohit is 40 Years and Present age of son is 16 years

Problem 4:

One year ago, the ratio of Gaurav’s and Sachin’s age was 6: 7respectively. Four years
hence, this ratio would become 7 : 8. How old is Sachin?

Solution :

1 Year ago Gaurav Age : Sachin age = 6 : 7

4 Years hence, Gaurav Age : Sachin age = 7 : 8
Sachin’s Age = ?

Let us assume Gaurav’s present age as x years and present age of Sachin as y years.

1 Year ago:
Gaurav’s age = x – 1 years
Sachin’s age = y – 1 years
As per Given: 1 Year ago Gaurav Age : Sachin age = 6 : 7

7(x -1 ) = 6 (y -1)

7x – 7 = 6y – 6

7x – 6y = 1 ---------------------------------------------Equation1
Four years hence:
Gaurav’s age = x + 4 years
Sachin’s age = y + 4 years
As per Given: 4 Years hence, Gaurav Age : Sachin age = 7 : 8

8x + 32 = 7y + 28
8x – 7y = - 4 ------------------------------------------------------Equation2

We can not solve Equation1 and Equation2 directly as nothing is common to cancel

We will multiply Equation1 by 8 and Equation2 by 7

Equation1 : 7x – 6y = 1 [Multiply by 8 both sides]

56x – 48y = 8 -----------------Equation3

Equation2 : 8x – 7y = -4 [Multiply by 7 both sides]

56x – 49y = -28 ------------------Equation4

56x – 48y = 8
- 56x – 49y = - 28
- + +
-----------------------------------------------
y = 36

Answer is Sachin’s present age is 36 years

Problem 5:

At present, the ratio between ages of Arun and Deepak is 4 : 3. After 6 years, Arun’s
age will be 26 years. What is age of Deepak as present?

Solution :

Present age of Arun : Present age of Deepak = 4 : 3

After 6 years Arun age = 26 Years
Deepak’s Present age = ?

After 6 years Arun’s age will be 26 years.

So at Present Arun’s age = 26 – 6 = 20 years

Given that Present age ratio Arun : Deepak = 4 : 3

Cross multiply to get answer

∗
Present age of Deepak = = = 15 Years

Answer is Deepak’s Present age is 15 years.

Problem 6:

Hitesh is 40 years old and Ronnie is 60 years old. How many years ago was their ratio
3:5?

a) 5 years b)10 years c)20 years d)37 years

Solution :

In such kind of scenario it is always better to go with options rather than solving
question.
How many years ago ratio was 3 : 5?
Hitesh present age = 40 years
Ronnie present age = 60 years

Option a: 5 years
5 years ago Hitesh age = 40 – 5 = 35
5 years ago Ronnie age = 60 – 5 = 55
35 : 55 = 7 : 11 [ So a is not answer]

Option b: 10 years
10 years ago Hitesh age = 40 – 10 = 30
10 years ago Ronnie age = 60 – 10 = 50
30 : 50 = 3 : 5 [ As it is matching with our expectation as 3: 5 ,so it is correct answer]

Answer is 10 Years ago ratio of Hitesh and Ronnie’s age was 3 : 5

Problem 7:

A man is 24 years older than his son. In two years, his age will be twice age of his son.
The present ages of Son is?

Solution :

Man present age = Son’s present age + 24

After 2 years, Man’s age = 2 * son’s age
Present age son =?

Let us assume present age of son is x years.

Man’s Present age = x +24

After 2 years:
Son age = x + 2
Man age = 2 (x + 2) = 2x + 4 ---------Equation1

However Man’s age after 2 years will be (x + 24) + 2= x +26 -----------Equation2

Equation1 and Equation2 both are equal and nothing but man’s age after 2 years

2x + 4 = x + 26
x = 22 [Present age of son]

Answer is Present age of Son is 22 years

Problem 8:

The total age of A and B is 12 years more than total age of B and C. C is how many
years younger than A?

Solution :

A age + B age = B age + C age + 12

C how many years younger = ?

Assume A age : A years, B: B years and C : C years

It is given that:

A + B = B + C + 12

A = C + 12

This means C is 12 years younger than A.

Answer is C is 12 years younger than A

Problem 9:

The sum of ages of father and his son is 45 Years. Five years ago, the product of their
ages was 34 years. The ages of son and father are respectively

Solution :

Present Father age + Son age = 45 years

5 years ago product of ages = 34

Present age of Father’s age and Son’s age = ?

Here we can take 2nd part to solve problem quickly.

5 years ago product of ages = 34

As to get product 34 there are only two options:

1) 17 * 2
2) 34 * 1

Let us take option 1 :

5 years ago Father’s age 17 and Son age 2

So present age Father’s age = 17 + 5 = 22

Present age Son = 2 + 5 = 7

Total of 22 and 7 is not 45

Option 2

5 years ago Father’s age 34 and Son age 1

So present age Father’s age = 34 + 5 = 39

Present age Son = 1 + 5 = 6

Total of 39 and 6 is 45

Answer is Present age of Father 39 Years and Son age is 6 years.