My grandmother was 9 times older than me 16 years ago. She will be 3 times of my age 8 years after from now. Eight years ago, the ratio of my age to that of my grandmother was?

1 : 5

16 years ago, My age = x years 

My grandmother's age = 9x year

After 8 years from the present, 

⇒ 9x + 16 + 8 = 3 ( x + 8 + 16)

⇒ 9x + 24 =  3x + 72 

⇒ 6x =  48 ⇒ x = 8 

Required ratio 8 years ago,

⇒ ( x + 8 )  :   ( 9x + 8 )

⇒ ( 8 + 8 )  :   ( 9 × 8 + 8 )

⇒        16    :    80

⇒         1     :    5