# Problems on Ages Tricks, Questions, Online Test, Video Lectures

Problems on ages is the part of Arithmetic Aptitude and important section of the competitive exam syllabus, to solve such questions, you are required the knowledge of linear equations. Sometimes it is easier to solve the questions by taking the given choices in account but this hit-and-trial method proves costly sometimes. Here we are giving you some easier as well as quicker way to solve this type of problems.

• If the current age is x, then n times the age is nx.
• If the current age is x, then age n years later/hence = x + n.
• If the current age is x, then age n years ago = x - n.
• The ages in a ratio a : b will be ax and bx.
• If the current age is x, then $\frac{1}{n}$ of the age is $\frac{x}{n}$

## Age Problems Involving A Single Person

Question: Five years ago, Arun’s age was half of the age he will be in 8 years. How old is he now?

Solution:
Step 1: Let x be Arun’s age now. Look at the question and put the relevant expressions above it.

Five year ago Arun's age: $x-5$
Arun’s age was half of the age he will be in 8 years: $\frac{1}{2}(x+8)$

Step 2: Write out the equation.

$x-5 = \frac{1}{2}(x+8)$

$x-5 = \frac{1}{2}x+4$

$x-5 = x-\frac{1}{2}x = 4 + 5$

$\frac{1}{2}x = 9$

$x = 18$

Answer: Arun is now 18 years old.

## Age Problems Involving More Than One Person

• Example 1

The age of the Mother 3 years ago was 7 times the age of his daughter. At present the Mother’s age is five times that of his son. What are the present ages of the Mother and the daughter?

Solution

Let the present age of daughter= x years.
Then, the present age of Mother= 5x years.
3 years ago,
7 (x – 3) = 5x – 3
or, 7x – 21 = 5x – 3
or, 2x = 18
∴ x = 9 years
Therefore, daughter’s age = 9 years.
Mother’s age = 45 years.

• Example 2

The average age of Salman, Rishi, Akashy, Amit and Ritik is 28 years. The average age of Amit and Rtik is 25 years. What is the average age of Salman, Rishi and Akashy ?

Solutions:
Here 5 persons' average ( Salman, Rishi, Akashy, Amit and Ritik) age is = 28 Years.

That means their total age = 5 X 28 = 140 Years.

Similarly, average age of two persons (Amit and Ritik) is 25 years.So their total age = 25 X 2 = 50 Years.

here 140 years is the total age of 5 persons ( Salman, Rishi, Akashy, Amit and Ritik)
50 years is the total age of 2 persons (Amit and Ritik)

So, the total age of Salman, Rishi, Akashy = Total age of (Salman, Rishi, Akashy, Amit and Ritik) - Total age of Amit and Ritik)

= 140-50 = 90 years.

Average age of these 3 persons = 90/3 The average age of Salman, Rishi and Akashy = 30 Years

• Example 3

At present the age of the Mother is five times that of the age of his son. Three years hence, the Mother’s age would be four times that of his son. Find the present ages of the Mother and the son.

Solution:

Let the present age of son = x years.
Then, the present age of father = 5x years.
3 years hence,
4(x + 3) = 5x + 3
or, 4x + 12 = 5x + 3
∴ x = 9 years.
Therefore, son’s age = 9 years and father’s age = 45 years.

• Example 4

The ratio between the ages of Ram and Rohan is 5:8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Ram ?

Solution :
Usually for these type of questions students start with present age as X and adding 5 to get the ages after 5 years and later solve those equations. But its very time taking procedure.

A simple logic here is if the age difference between you and your friend is 8 years, after 5 or 10 years also the difference will be same.

the ratio between their ages is 5 : 8

That means their actual ages will be some 5X and 8X

Then the difference between their ages is 5X-8X
in this question it is given that the difference is 12 years

= 5X-8X = 12
= 3X=12 = X = 4

So obviously Ram's age = 5(4) = 20

• Example 5

Yogesh is 30 years younger than his Father. Five years ago, Yogesh was 1/4 as old as his father was. How old is Yogesh today ?

Solution :

5 years ago the ratio between their ages was Yogesh : Mother = 1X : 4X

we know that Yogesh is 30 years younger than his mother. That means the difference between their ages is 30.

= 3X = 30
= X = 10.

But this is the age of 5 years ago. So, the present age will be = 10+5 = 15 Years

Problems on Age