Sixteen years ago, my grandmother was 9 times as old as I was. Eight years from now, she will be 3 times as old as I will be. What was the ratio of my age to my grandmother's age eight years ago?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 5
Take my present age as \(x\) and grandmother's as \(g\), turn each statement into an equation, and solve the two together.
Sixteen years ago: \(g-16=9(x-16)\), so \(g=9x-128\)
Eight years hence: \(g+8=3(x+8)\), so \(g=3x+16\)
\(9x-128=3x+16\), so \(6x=144\) and \(x=24\)
\(g=3\times24+16=88\)
Eight years ago: my age \(=16\), grandmother's age \(=80\)
Ratio \(=16:80=1:5\)