I Have solved the problem.
For any newbie, here is what I did,
var
DbPath : String;
begin
//adotable1.Connection := adoconnection1;
DbPath := ExtractFilePath(Application.ExeName) + ExtractfileName('QuickiesContest.mdb');
adoconnection1.ConnectionString :=
'Provider=Microsoft.Jet.OLEDB.4.0;Data Source=' + DbPath ;
end;