My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was:
3 : 8
2 : 5
1 : 2
1 : 4
1 : 5
Solution
16 years ago,
My age $=x$ years
My grandfather's age $=9x$ years
After 8 years from the present,
$9x + 16 + 8 = 3(x+8+16)$
$\Rightarrow 9x + 24 = 3x + 24 + 48$
$\Rightarrow 9x-3x = 72-74 \Rightarrow 6x = 48$
$\Rightarrow x = \dfrac{48}{6}=8$
Required ratio 8 years ago,
$=(x + 8) : (9x + 8)$
$=(8 + 8) : (9\times 8 + 8)$
$16 : 80 = 1 : 5$