Total age of two members in a family four years hence will be 64 years. Four years back their ages was in the ratio 3 : 1. What is the age of the younger of the two?

let the ages of two persons be x and y

4 years back their ages was in the ratio 3 : 1

$$ \frac{x - 4}{y - 4} = \frac{3}{1} $$

solving 

x - 4 = 3y - 12

3y - x = 8...........(1)

Total age of two members in a family four years hence will be 64 years

x + y + 8 = 64

x + y = 56............(2)

from (2)  x = 56 - y

substitute x in (1)

8 = 3y - (56 -y)

solving y = 16

x + 16 = 56

x = 40

therefore age of younger person is 16