$$Statement\ 1\ =>\ \left(a\right)\left(c\right)=0$$
$$for\ the\ product\ of\ 2\ numbers\ to\ =0,\ one\ or\ both\ of\ the\ number\ will\ be\ =\ 0$$
$$so\ it\ is\ either\ a<c,\ a>c\ or\ a=c$$
$$\sin ce\ there\ is\ no\ definite\ value\ for\ a\ and\ c,\ statement\ 1\ is\ NOT\ SUFFICIENT$$
$$Statement\ 2\ =>\ a+b=0$$
$$a=-b\ i.e\ a\ is\ the\ negative\ value\ of\ b$$
$$but\ there\ is\ no\ \inf ormationn\ about\ the\ value\ of\ c\ so\ statement\ 2\ is\ NOT\ SUFFICIENT$$
$$Combining\ both\ statements\ together\ =>$$
$$from\ statement\ 2\ =>a\ is\ negative\ $$
$$by\ considering\ statement\ 1,\ c\ has\ to\ be\ zero\ for\ \left(a\right)\left(c\right)\ to\ be\ =0$$
$$Therefore,\ a<c$$
$$both\ statemets\ together\ ARE\ SUFFICIENT$$
$$Answer\ =\ C$$
