## Problems Based on years ago Ages Shortcut Tricks

**Example 1 :**

Suman and Bivash is 50 years old and 70 years old . How many years before was the ratio of their ages 3 : 5 ?

**Answer :**

Their ratio was 3 : 5 , Y years before ,

So, 50 – y / 70 – y = 3 / 5

5 ( 50 – y ) = 3 ( 70 – y )

250 – 5y = 210 – 3y

2y = 40

y = 20 years.

**Example 2 :**

The present ratio of ages of P & Q is 4 : 6 . If the sum of present ages of P & Q is 50 years. Find the ages of P & Q before 4 years.

**Answer:**

Let ages of P & Q is x , so P & Q ages are 4x and 6x Gradually.

Now according to question Sum of present ages ,

4x + 6x = 50, 10x = 50, x = 5 years, (We got the value of x = 5)

And than the present age of P is = 4x = 4 x 5 = 20 years.

So, years ago the age of P = ( 20 – 4 ) = 16 years, and present age of Q is = 6x = 6 x 5 = 30 years.

So, years ago the age of Q = (30 – 4 ) = 26 years.

**Example 3 :**

Reeya is 28 years old and Rajib is 12 years . In how many years will Reeya be twice as old as Rajib ?

**Answer :**

Let Reeya be in x years . Then

( 28 + x ) = 2 ( 12 + x )

28 + x = 24 + 2x

x = 4 years .

**Example 4 :**

The ratio of ages of P & Q after 5 years will be 3 : 5 . If the sum of ages of P & Q at present is 38 years . Find the ages of P & Q before 5 years .

**Answer :**

Let the ages of P & Q are 3x and 5x respectively after 5 years .

( 3x – 5 ) + ( 5x – 5 ) = 38 years

6x – 10 = 38 years

8x = 48 years

x = 6

The ages of P after 5 years

= 6 x 3

= 18 years

Then the ages of Q after 5 years

6 x 5 = 30 years

The ages of P & Q before 5 years is

P = ( 18 – 10 ) = 8 years

Q = ( 30 – 10 ) = 20 years .