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?

The total age of two family members four years hence will be 64 years.

Four years ago, their ages were in the ratio $3:1$. 

Solution: 

Let the present age of two persons be x and y.

So, 

( x + 4) +  ( y + 4) = 64 

x + y = 56 ........(i) 

Four years ago, 

​$$\frac{ x - 4}{y - 4} = \frac{3}{1} \\ x -4 = 3y - 12 \\ x - 3y = -8 .......(ii)$$ 

Substacting eqn(i) and (ii) .

​$$x+y=56\\ \underline {\pm x\mp3y=\mp8} \\ 4y\ \ \ =64 \\ y = 16$$ 

Putting y = 16 in eqn(i) 

x = 56 - 16 = 40

Thus, the age of younger of two is 16 years.