To complete a task in 16 days a company needs 5 people each working for 6 hours per day. The company decides to have 8 people each working for 4 hours per day assuming that each person works at the same rate. How many days will the task take to complete?

If 5 people each works 6 hours per day for 16 days, then total number of hours required to complete the work is $(6\times 16\times 5)=480$ hours.
Now, the company decides to have 8 people each working for 4 hours per day, then if we assume that each person works at the same rate, then n number of days will be requires to complete the task.
So, the total number of hours required is $(4\times n\times 8)$.
Hence, , $4\times n\times 8=480$
$n=15$ days.
Therefore, 15 days will be required to complete the task.