In this section, the following topics are discussed with examples

### INTRODUCTION

The topic of Ages is a kind of problem formulation which deals with the relationship between the persons in terms of linear equations.

### How to formulate the AGES problems:

Ages problem are formulated on the basis of certain clues or keywords that are all given below.

1) Let as considered the current age as X, then “n” times the X value is denoted as nX.

2) If the “X” age is n times twice than the “Y” age, then X = nY

3) If “X” age is 10 years before, then the condition is (X-10). If X age is 10 years after then the condition is (X+10).

4) If the product of X and Y is “n” , then the equation is X x Y =n

## Youth is the gift of nature, but age is a work of art.

Stanislaw Jerzy Lec

#### Example

1) Raju is 4 years older than sunil who is twice as old as vinoth. If the total ages of Raju,Sunil and Vinoth is 24, then how old is sunil?

Sol:

Let us considered the Raju’s present age is “R”, Sunil’s present age is “S” and vinoth’s present age is “V”.

R is 4 times older than sunil, so the equation is, R= S+4………..eq(1)

S is twice as old as vinoth , so the equation is . S= 2V………..eq(2)

Total ages of Raju, Sunil and Vinoth is 24, i.e., R+S+V=24………..eq(3)

Subtitute the equation (2) in eq (1)

R= 2V+4………………….eq(4)

R+S+V=24………………….eq(3)

Substitute eq(4) and eq (2) in eq (3)

2V+4+2V+V=24

5V=20

V=4

Therefore Vinoth age is 4 yrs old

In order to found out the sunil age, subtitute the Vinoth age in eq(2)

S=2V

S=8

Therefore Sunil age is 8 yrs old

### 2) Balu is 14 years older than his son. In four years his age will be twice the age of his son.Then what is the present age of son?

SOLUTION:

Let us considered the present age of Balu is “B” and the present age of his son is “S”

Balu is 14 years older than his son,i.e., B= S+14……….eq(1)

In four years his age will be twice the age of his son. i.e., B+4 = 2(S+14)……eq(2)

Substitute the eq(1) in eq(2)

S+14+4 = 2(S+14)

S+14+4=2S+28

S=10

There fore the present age of son is 10

### 3) The respective ages of Babu and Ramesh is 8:10.If Babu is 8 years younger than Ramesh then how old is Babu?

SOLUTION:

Let us considered the present age of Babu and Ramesh is “B” & “R”.

From these sentence, Babu is 8 years younger than Ramesh it is clearly deoted that Ramesh is the elder one and Babu is the younger one and their age differences is 8 years.

So let we take a common term for both Babu and Ramesh is “X”.

Ramesh is 8 years elder than Babu, so let we take the Ramesh age is (X+8)

Babu and Rames ages are (X, X+8)

The respective age of Babu and Ramesh is 8:10

Therefore,

X/(X+8) = 8/10

10X=8X+64

2X=64

X=32

Babu’s age is (X=32), where Ramesh age is (X+8= 40)

### PRACTICE

1) Raju is 20 years old and Arjun is 40 years old, How many years ago was the ratio of their ages 9:6?

2) Ten years hence, the Mother’s age will be twice the sum of ages of her daughters.The mother’s present age is six times the sum of the ages of her daughters.What is the age of mother.