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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