Find the ratio of future ages

At present: $\dfrac{K}{M}=\dfrac{1}{2}$ $[1]$

8 years ago: $\dfrac{K-8}{M-8}=\dfrac{1}{3}$ $[2]$

From $[1]$ , we get: $M=2K$

From $[2]$ , we get: $3K - 24 = M - 8$

Substitute $M=2K$ into the above equation.

$3K = 2K + 16$

$K = 16$

It follows that,

$M = 32$

16 years form now: $\dfrac{K+16}{M+16}=\dfrac{16+16}{32+16}=\dfrac{32}{48}=\large{\boxed{\color{#3D99F6}\dfrac{2}{3}}}$

K : M

1 : 3

+8 for each

1 : 2= 2 : 4

1unit=8

16 : 32

+16 for each

32 : 48 = 2 : 3

8 years ago is 1:3

Now is 2:4

8 years later is 3:5

16 years later is 4:6