Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. 8 years ago, what was the ratio of Tanya's age to that of her grandfather ?

Answer: Option D

16 years ago, let T = x years and G = 8x years
After 8 years from now,
T = (x + 16 + 8) years and G = (8x + 16 + 8) years
$$\begin{array}{rl}& \therefore \text{8x + 24 = 3}\left(x+24\right)\\ & \Rightarrow 8x-3x=72-24\\ & \Rightarrow 5x=48\\ & 8\text{years ago,}\\ & \frac{\text{T}}{\text{G}}\\ & =\frac{x+8}{8x+8}\\ & =\frac{\frac{48}{5}+8}{8\times \frac{48}{5}+8}\\ & =\frac{48+40}{384+40}\\ & =\frac{88}{424}\\ & =\frac{11}{53}\end{array}$$