Four workers can build a stage in 10 eight-hour days. At the same rate, how many workers will it take to build the stage in 5 eight-hour days?

To get it done in HALF the time will take TWICE as many workers.      8 workers.

ElectricPavlov is correct.

One way to analyze the problem:  

     Each worker worked 10 eight-hour days for a total of 80 hours (10 x 8).

     Since there were four workers, they worked a total of 320 hours.

If you want to build the stage in 5 eight-hour days, each worker needs to work 40 hours (5 x 8).

The total number of hours needed is still 320 hours; since each worker works 40 hours, calculate  320 / 40 to get 8.

You will need 8 workers.