Tanya's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago?

Let Tanya's current age be $x$

$16$ years ago:

$y - 16 = 8(x - 16)$ where $y$ is grandfather's current age

$8$ years from now:

$y + 8 = 3(x + 8)$

From first equation:

$y - 16 = 8x - 128$

$y = 8x - 112$ ... $(1)$

From second equation:

$y + 8 = 3x + 24$

$y = 3x + 16$ ... $(2)$

Equating $(1)$ and $(2)$:

$8x - 112 = 3x + 16$

$5x = 128$

$x = \frac{128}{5}$

Substituting in equation $(1)$:

$y = 8(\frac{128}{5}) - 112$

$y = \frac{1024}{5} - 112$

$y = \frac{1024-560}{5}$

$y = \frac{464}{5}$

$8$ years ago:

Tanya's age = $\frac{128}{5} - 8 = \frac{128-40}{5} = \frac{88}{5}$

Grandfather's age = $\frac{464}{5} - 8 = \frac{464-40}{5} = \frac{424}{5}$

Ratio = $\frac{88}{5} : \frac{424}{5}$

$= 88 : 424$

$= 11 : 53$

Therefore, the ratio of Tanya's age to her grandfather's age $8$ years ago was $11 : 53$.