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1. 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 ?

A. 1 : 2

B. 1 : 5

C. 3 : 8

D. None of these

Solution:

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{aligned} ∴ 8x + 24 = 3 (x + 24) \\ \Rightarrow 8 x - 3 x = 72 - 24 \\ \Rightarrow 5 x = 48 \\ 8 years ago, \\ \frac{T}{G} \\ = \frac{x + 8}{8 x + 8} \\ = \frac{\frac{48}{5} + 8}{8 \times \frac{48}{5} + 8} \\ = \frac{48 + 40}{384 + 40} \\ = \frac{88}{424} \\ = \frac{11}{53} \end{aligned}

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