Problems on Ages

Problems on Ages

In Below example we learn Power, Variable and Co-Efficient.

Example : 

Here, 2 = Power,

          5 = Co-Efficient,

          x = Variable.

Solve Simple Equations: 

Example:

5x - 10 = 2x + 5

5x - 2x = 5 + 10

3x = 15

x = 5

Example:

x + 3(x + 1) = 27

x + 3x + 3 = 27

4x = 27 -3

4x = 24

x = 6

Solve Examples with Ages :

Example: 1

A Father is now 3 times as old as his Son. 5 years ago he was 4 times as old as his son. Find Their present ages. 

Solution :

Son          :  Present age = x               5 years ago = x - 5

Father      :  Present age = 3x             5 years ago = 3x - 5

So we are simplify this equations

3x - 5 = 4(x - 5)

3x - 5 = 4x - 20

4x - 3x = 20 - 5

x = 15

So, Present age of Son = x  = 15

Present age of Father = 3x = 3(15) = 45

Example: 2

A man is 6 times as old as his Son. 2 years hence he will be 5 times as old as his son. Find their present ages.

Solution :

Son          :  Present age = x               2 years hence = x + 2

Father      :  Present age = 6x             2 years hence = 6x + 2 

6x + 2 = 5(x + 2)

6x + 2 = 5x + 10

6x - 5x = 10 - 2 

x = 8

So, Present age of Son = x  = 8

Present age of Father = 6x = 6(8) = 48

Example: 3 

The ages of 2 persons differ by 20 years. 5 years ago, the elder one be 5 times as old as the younger One. Find their Present ages.

Solution :

Older     : Present age = x                     5 years hence = x - 5 

Younger : Present age = x - 20             5 years hence = x - 20 - 5  = x - 25

(x - 5) = 5(x - 25)

x - 5 = 5x -125

125 - 5 = 5x - x

120 = 4x

x = 30

So, Present age of Elder = x  = 30

Present age of Younger = x - 20 = 30 - 20 = 10