## 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 ?

**Answer :**

**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.

**Answer :**

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.

**Answer :**

**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 ?

**Answer :**

**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 ?

**Answer :**

**Step 1:**Let the A’s age and B’s age be 6x and 7x years respectively . Then , 7x – 6x = 4 . S0, x = 4

**Step 2 :** Required ratio = ( 6x + 4 ) : ( 7x + 4 ) = 28 : 32 = 7 : 8

**Example 6:**

The ratio of mother age to his son’s age is 7 : 3 . The product of their ages is 756 . The ratio of their ages after 6 years wil be ?

Answer :

**Step 1 :** Let the present ages of the mother and son be 7x and 3x years respectively .

Then , 7x X 3x = 756

21×2 = 756

= x2 = 36

= x = 6 .

**Step 2 :** Required ratio = (7x + 6 ) : ( 3x + 6 ) = 48 : 24 = 2 : 1 .