Question
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
$$\eqalign{
& \therefore {\text{8x + 24 = 3}}\left( {x + 24} \right) \cr
& \Rightarrow 8x - 3x = 72 - 24 \cr
& \Rightarrow 5x = 48 \cr
& 8{\text{years ago,}} \cr
& {\text{ }}\frac{{\text{T}}}{{\text{G}}} \cr
& = \frac{{x + 8}}{{8x + 8}} \cr
& = \frac{{\frac{{48}}{5} + 8}}{{8 \times \frac{{48}}{5} + 8}} \cr
& = \frac{{48 + 40}}{{384 + 40}} \cr
& = \frac{{88}}{{424}} \cr
& = \frac{{11}}{{53}} \cr} $$
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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
$$\eqalign{
& \therefore {\text{8x + 24 = 3}}\left( {x + 24} \right) \cr
& \Rightarrow 8x - 3x = 72 - 24 \cr
& \Rightarrow 5x = 48 \cr
& 8{\text{years ago,}} \cr
& {\text{ }}\frac{{\text{T}}}{{\text{G}}} \cr
& = \frac{{x + 8}}{{8x + 8}} \cr
& = \frac{{\frac{{48}}{5} + 8}}{{8 \times \frac{{48}}{5} + 8}} \cr
& = \frac{{48 + 40}}{{384 + 40}} \cr
& = \frac{{88}}{{424}} \cr
& = \frac{{11}}{{53}} \cr} $$
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