Question

kartik is younger than son by 12 years. If 6 years ago, ratio of their ages was 3:5,find the ratio of their ages after 6 years from now

Answer 1

let kartik age to be x 
son will be x + 12
6 years ago = x + 12 - 6 and x - 6 
x - 6 / x + 6 = 3 / 5
5 [ x - 6 ] = 3 [ x + 6 ]
5x - 30 = 3x + 18
5x - 3x = 30 + 18
2x = 48
x = 24
present age  of kartik is 24 years
present age of son = 24 + 12 = 36

after 6 years = son and kartik respectively are 42 and 30 years old..

hope this was helpful..

Answer 2

Here's your answer,
Let, Son's age be x
Kartik's age be x-12

Before 6 years,
Son's age = x-6
Kartik's age = x-12-6
= x-18

ATQ

$\frac{x - 18}{x-6} = \frac{3}{5} \\ \: 5x - 90 = 3x-18 \\ 5x - 3x = 90-18 \\ 2x = 72 \\ x = \frac{72}{2} \\ x = 36$

Now,
Son's present age =36
Kartik's present age = 24

After 6 years,

Son's age =42
Kartik's age = 30
Ratio of their age = 30/42
= 5:7

Hope it helps!!!!!