很少見 spend time in doing sth 這種說法.
一般而言,spend time 后如果直接跟“動名詞”（v+ing）,既不用 in 也不用 on.
如果后面跟的是地點狀語,用 in；如果跟的是事或人,用 on.例：
My parents spent their vacation in Paris.
I spent all my resources on futile projects.
John spent most of his time on his girlfriend.??????????????????????spend ??in) doing????????????????????λ????????????? in???????á??????spend money/time ??in?? doing,??????????á????????????????????????????y????????????????? on?????????????????????????????????У?????????????????????? in ???