RMO 2016 D3

The precent ages in years of two brothers $A$ and $B$ ,and their father $C$ are three distinct positive integers $a ,b$ and $c$ respectively .Suppose $\frac{b-1}{a-1}$ and $\frac{b+1}{a+1}$ are two consecutive integers , and $\frac{c-1}{b-1}$ and $\frac{c+1}{b+1}$ are two consecutive integers . If $a+b+c\le 150$ , determine $a,b$ and $c$ .