If six persons can complete a job in eight days, how many days will it take four persons working at the same speed?

To determine how many days it will take four persons to complete the same job, we first need to understand the relationship between the number of workers, the amount of work done, and the time taken.

If six persons can complete a job in eight days, we can calculate the total amount of work done in person-days. The total amount of work is represented by multiplying the number of persons by the number of days they work. In this case:

Total Work = Number of Persons × Number of Days

Total Work = 6 persons × 8 days = 48 person-days

Now, if we have four persons working on the same job, we need to find out how long it will take them to complete 48 person-days of work. Let "D" represent the number of days it will take for four persons to complete the job. The equation will be:

Total Work = Number of Persons × Number of Days

48 person-days = 4 persons × D days

To find D, we can rearrange the equation:

D = Total Work / Number of Persons

D = 48 person-days / 4 persons = 12 days

Thus, it will take four persons 12 days to complete the job, making that the correct