Alice can do a job in $$40$$ days and Bob can do it in $$60$$ days. Now they\textquotesingle re working together, but Alice takes some days off in the middle of the job. If they finish the job by the end of the $$27^{}\text{th}$$~day, how many days does Alice take off? 
Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems