If 80 persons can perform a piece of work in 16 days of 10 hours each, how many men will perform a piece of work twice as great in tenth part of the time
working 8 hours a day supposing that three of the second set can do as much
work as four of the first set?

The number of men needed to perform a piece of work twice as great in tenth part of the time  working 8 hours a day supposing that three of the second set can do as much  work as four of the first set is:

1200 men.

Step-by-step explanation:

To find the answer, first, we're gonna find how many hours take to make the piece of work in 16 days, taking into account each day just has 10 hours:

Number of hours to make a piece of work = 16 * 10 hoursNumber of hours to make a piece of work = 160 hours.

Now, we divide the total hours among the number of persons:

Equivalence of hours per person = 160 hours / 80 persons.Equivalence of hours per person = 2 hours /person

This equivalence isn't the real work of each person, we only need this value to make the next calculations. Now, we have a piece of work twice as great as the first, then, we can calculate the hours the piece of work needs to perform it (twice!):

Number of hours to make the second piece of work = 160 hours * 2Number of hours to make the second piece of work = 320 hours

We need to make this work in tenth part of the time working 8 hours a day, it means:

Time used to the second work = 320 hours / 10Time used to the second work = 32 hours Time used to the second work = 32 hours / 8 hours (as each day has 8 hours)Time used to the second work = 4 days

Now, we know three of the second set can do as much  work as four of the first set, taking into account the calculated equivalence, we have:

Work of four workers of first set = Work of three workers of second setWork of four workers of first set = Equivalence * 4 persons.Work of four workers of first set = 2 hours /person * 4 personsWork of four workers of first set = 8 hours.

So, three persons of the second set can make a equivalence of 8 hours. At last, we calculate all the number of workers we need in a regular time:

Number of needed workers in a regular time = (320 hours / 8 hours) * 3 persons.Number of needed workers in a regular time = 40 * 3 personsNumber of needed workers in a regular time = 120 persons

Remember we need to perform the job not in a regular time, we need to perform it in tenth part of the time, by this reason, we need 10 times the number of people:

Number of needed workers in tenth part of the time = 120 persons * 10Number of needed workers in tenth part of the time = 1200 persons

With this calculations, you can find the number of men needed to perform a piece of work twice as great in tenth part of the time  working 8 hours a day supposing that three of the second set can do as much  work as four of the first set is 1200 persons.

A because 10 percent out of 1200 is 10