## 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 ?
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.
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 ?
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 .