Question 72

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.

Solution
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Let Current ages of Tanya & her grandfather be X, Y respectively.
Given :
16 yrs ago : (Y-16)  =  8(X-16)
8 yrs later : (Y+8) =  3(X+8)

By solving above both equations we arrive at X = $$\dfrac{\ 128}{5}$$ , Y = $$\ \dfrac{\ 464}{5}$$

Therefore 8 yrs ago the ratio will be $$\dfrac{\ X-8}{Y-8}$$ = $$\dfrac{\ 88}{424}$$ = $$\dfrac{\ 11}{53}$$

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