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

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 + 24 = 3x + 72
$\Rightarrow$  9x – 3x = 72 – 24

$\Rightarrow$ 6x = 48

$\Rightarrow$ x= 8

Required ratio 8 years ago,
= (x + 8) : (9x + 8)
= (8 + 8) : (9 × 8 + 8)
= 16 : 80 = 1 : 5

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