Question : Sixteen years ago, my grandfather was 9 times older than me. Eight years from now, he will be 3 times my age. Determine the ratio of my age to my grandfather's age eight years ago.
Option 1: 3 : 8
Option 2: 2 : 5
Option 3: 1 : 2
Option 4: 1 : 5
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Correct Answer: 1 : 5
Solution : 16 years ago, let my age and my grandfather's age be $x$ years and $9x$ years respectively. According to the question, $9x+16+8=3(x+16+8)$ ⇒ $9x+24=3x+48+24$ ⇒ $6x=48$ ⇒ $x=8$ Required ratio 8 years ago, = $(x+8):(9x+8)$ = (8 + 8) : (9 × 8 + 8) = 16 : 80 = 1 : 5 Hence, the correct answer is 1 : 5.
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