My grandfather was 9 times older than me 16years 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:  (1) 3: 8 (2) 2: 5 (3) 1: 2 (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)

⇒9x+ 24 = 3x+ 24 + 48

⇒9x+24=3x+72

⇒9x- 3x= 72 -24 

⇒6x= 48

⇒x=48/6 = 8

Required ratio 8 years ago,

= (x+ 8) : (9x+ 8)

= (8 + 8) : (9 * 8 + 8)

= 16:80 = 1: 5

Then the option is (4) 1:5