Question

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?

Answer 1

Grandfather is `65` years old.
Grandson is `5` years old.

Explanation:

Let the grandfather's age be `x`
and the grandson's age be `y`.

We are told
`color(white)("XXX")x=15y`
and
`color(white)("XXX")y+10=3/17(x+10)`

`color(white)("XXXXXX")rarr 17y+170=3x+30`

`color(white)("XXXXXXXXXXXXXX")=45y+30` (since `x=15y`)

`color(white)("XXXXXX")rarr140=28y`

`color(white)("XXXXXX")rarry=5`

`color(white)("XXX")x=15y=65`