Each one of six men independently can complete a work in 27 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the sixth day, six person continued working as a team. In how many days, will the work be completed?

7

Here, work is completed by each in 27 days

So, let the total work is = 27,

Therefore, the efficiency of each person = 1 w/d

Now, ATQ

1st day work ( by 1 person)  = 1

2nd day work ( by 2 person)  = 2

3rd day work ( by 3 person)  = 3

4th day work ( by 4 person)  = 4

5th day work ( by 5 person)  = 5

6th day work ( by 6 person)  = 6

Total work done in 6 days = 1 + 2 + 3 + 4 + 5 + 6 = 21

Remaining work = 27 - 21 = 6

7th day work ( by 6 person)  = 6

Therefore, the work will be completed in total 7 days.