Question

A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

Answer 1

boy is `9` years old
sister is `12` years old

Explanation:

Let the age of boy be `b` and the age of his sister be `s`
So given `s=b+3`
and `b-3=2/3(s-3)`
or
`3(b-3)=2(s-3)`
by putting `s=b+3` in the equation `3(b-3)=2(s-3)`
We get
`3(b-3)=2(b+3-3)`
`3b-9=2(b+0)`
or
`3b-9=2b`
or
`3b-2b=9`
or
`b=9`-------------boy is `9` years old
Since `s=b+3`
or
`s=9+3`
or
`s=12` -------------------------sister is `12` years old