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

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

Apr 19, 2016

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

#### Explanation:

Let $G F$ and $G S$ 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: $G F = 15 G S$ (1)

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

Therefore: $\frac{3}{17} \left(G F + 10\right) = G S + 10$ (2)

Substituting (1) in (2)

$\frac{3}{17} \left(15 G S + 10\right) = G S + 10$

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

$28 G S = 140$

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

Substituting for GS in (1)

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