Sudha's grandfather was 8 time older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Sudha's age to that of her grandfather?

Let us assume 16 years ago, the age of Sudha and her grandfather were x and 8x years respectively; then
Present age of Sudha = x + 16
Present age of her grandfather = 8x + 16
After 8 years age of sudha from now = x + 16 + 8
After 8 years age of grandfather from now = 8x + 16 + 8
now according to question,
He would be 3 times of her age 8 years from now.
3(x + 16 + 8) = 8x + 16 + 8
? 3x + 72 = 8x + 24
? 5x = 48
? x = 48/5
Eight years ago , sudha age = x + 16 - 8 = x + 8
Eight years ago , grandfather age = 8x + 16 - 8 = 8x + 8
Hence, required ratio = (x + 8) / (8x + 8 )
Put the vale of x , we will get
? required ratio = (48/5 + 8) / ( 8 x 45/5 + 8)
? required ratio = ((48 + 40)/5) / ( (8 x 45 + 40)/5)
? required ratio = (88/5) / ( 400/5)
? required ratio = 88 / 400
? required ratio = 11 : 50