## Problems Based on after years Ages Shortcut Tricks

### Example 1 :

The sum of present ages of a father and his son is 60 years, 6 years ago, father’s age was five times the age of the son. What will be After six years son’s age will be ?
Step 1: let present age of son and father is x and (60 – x ) years, Then,
( 60 – x ) – 6 = 5 (x – 6 )
54 – x = 5x – 30
6x = 84
x = 14 years.
Step 2: Son’s age after six years is ( x + 6 ) = 14 + 6 = 20 years,

### Example 2 :

Ratio of present ages of C & D is 4 : 6 . The present age of C is 40 years. Find the age of D after 6 years.
First we do Traditional way than we do shortcut way.
Let the ages of C & D are 4x and 6x.
Hence,C = 4x = 40, = x = 10, ( So we get the value of x )
So the present age of D is = 6x = 6 X10 = 60 years, hence the age of D is  after 6 years 60 + 6 = 66 years.

### Example 3 :

Ratio of present ages of C & D is 4 : 6 . The present age of C is 40 years. Find the age of D after 6 years.
Step 1: C : D = 4: 6, According to Question C present age is = 40 years.
Step 2: So the D present age  we get ( 40 / 4 )X 6 = 10 X 6 = 60 years.
Step 3: After 6 years the age D is 60 + 6 = 66 years.

### Example 4 :

The ratio of present ages of two students is 1 : 2 and 5 years back , the ratio was 1 : 3 . What will be the ratio of their ages after 5 years ?
Step 1 : Let the present ages of the two students be x years and 2x years respectively .
Then , x – 5 / 2x – 5 = 1 / 3
= 3 ( x – 5 ) = ( 2x – 5 ) = x = 10 . So , replace value of x = 10 .
Step 2 : Required ratio =( x + 5 ) : ( 2x + 5 ) = 15 : 25 = 3 : 5 .

### Example 5 :

The ratio between the present ages of A and B is 6 : 7 . If B is 4 years old tha A , What will be the ratio of the ages of A and B after 4 years ?