Question

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?

Answer 1

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.

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 hours
• Number 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 * 2
• Number 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 / 10
• Time 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 set
• Work of four workers of first set = Equivalence * 4 persons.
• Work of four workers of first set = 2 hours /person * 4 persons
• Work 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 persons
• Number 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 * 10
• Number 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.