Grandfather is $15$ $15$ time the age of his grandson today, in $10$ $10$ years the grandson will be $\frac{3}{17}$ $3/17$ the age of the grandfather. How old are the grandfather and grandson?

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Answer 1 · 2016-04-19T01:05:39

Today Grandfather is 75 years old, Grandson is 5 years old.

Let $G F$ $GF$ and $G S$ $GS$ be the current ages in years of the Grandfather and Grandson respectively

We are told that Grandfather is 15 times the age of the Grandson today

Therefore: $G F = 15 G S$ $GF = 15GS$ (1)

We are also told that in 10 years the Grandson will be $\frac{3}{17}$ $3/17$ the age of the Grandfather.

Therefore: $\frac{3}{17} (G F + 10) = G S + 10$ $3/17(GF+10) = GS+10$ (2)

Substituting (1) in (2)

$\frac{3}{17} (15 G S + 10) = G S + 10$ $3/17(15GS + 10) = GS+10$

$45 G S + 30 = 17 G S + 170$ $45GS+30 = 17GS+170$

$28 G S = 140$ $28GS = 140$

$G S = \frac{140}{28} = 5$ $GS=140/28 = 5$ Years

Substituting for GS in (1)

$G F = 15 \cdot 5 = 75$ $GF= 15 * 5 = 75$ Years

Grandfather is 151515 time the age of his grandson today, in 101010 years the grandson will be 3/173173/17 the age of the grandfather. How old are the grandfather and grandson?