Sixteen years ago, Tanay's grandfather was $8$ times older to her. $8$ years from now h e would be $3$ times for her age. Eight years ago. what was the ratio of Tanya's age to that of her grandfather?

Let Tanya's present age be T and her grandfather's present age be G. Sixteen years ago, G - 16 = 8(T - 16), and 8 years from now, G + 8 = 3(T + 8). Solving this system of linear equations yields T = 24 and G = 72. Eight years ago, Tanya was 16 and her grandfather was 64, making their ratio 1 : 4, which is not listed among the choices. The correct answer is none of these.

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