The old need 后加looking after 还是being looked after

being looked after
老人需要被照顾,使被动语态

the elders need looking after
the elders need to be looked after
the elders need being looked after
语法上都是对的

need应该加不定式to,还要被动语态,那就是The old need to be looked after

need to be looked after 和 need being looked after都对，need后可加动词ing也可以加不定式
即：need to be done
need being done
都是“需要被做”的意思

我觉得应该是looking after
比如My car needs repairing.并不需要用被动

being looked after
是老人被照顾 不是照顾别人,故用被动形式