Same persons can do a piece of work in 12 days. Two times the number of such persons willdo half of that work in:1. 6 days 2. 4 days3. 3 days 4. 12 days

To solve this problem, we can use the concept of person-days of work. Let's assume that one person can do the entire work in 12 days. This means that in one day, one person can do 1/12th of the work.

Now, let's consider the first scenario where two times the number of persons will do half of the work in 6 days. If one person can do 1/12th of the work in one day, then two times the number of persons will be able to do 2/12th or 1/6th of the work in one day. Therefore, they will be able to complete half of the work in 6 days.

Similarly, in the second scenario where two times the number of persons will do half of the work in 4 days, they will be able to complete 1/4th of the work in one day.

In the third scenario, where two times the number of persons will do half of the work in 3 days, they will be able to complete 1/3rd of the work in one day.

Lastly, in the fourth scenario where two times the number of persons will do half of the work in 12 days, they will be able to complete 1/12th of the work in one day.

So, the answers to the given scenarios are:

1. 6 days
2. 4 days
3. 3 days
4. 12 days