Get "start of current year":
NSCalendar *cal = [NSCalendar currentCalendar];
NSDate *now = [NSDate date];
NSDate *startOfYear;
[cal rangeOfUnit:NSYearCalendarUnit startDate:&startOfYear interval:NULL
forDate:now];
// startOfYear represents now the start of the current year.
Add 205 days:
int dayofyear = 205;
NSDateComponents *comp = [[NSDateComponents alloc] init];
[comp setDay:dayofyear];
NSDate *newDate = [cal dateByAddingComponents:comp toDate:startOfYear options:0];