High School

100 men working 8 hours a day can complete a piece of work in 30 days.

How many men are required to complete the work in 20 days working 12 hours per day?

A. 100
B. 80
C. 75
D. 115

Answer :

To solve this problem, we need to determine how many men are required to complete the work in 20 days if they work 12 hours a day, given that 100 men can complete it in 30 days working 8 hours a day.

First, we calculate the total amount of work needed to be completed in terms of man-hours.

  1. Calculate Total Work in Man-Hours:

    The total work done is the product of the number of men, hours per day, and number of days.

    [tex]\text{Total Work} = 100 \text{ men} \times 8 \text{ hours/day} \times 30 \text{ days} = 24,000 \text{ man-hours}[/tex]

  2. Determine New Work Conditions:

    Now, we want this same work to be completed in 20 days, by working 12 hours each day.

  3. Calculate Required Number of Men:

    Let [tex]n[/tex] be the number of men required to complete the same amount of work under these new conditions. The equation for the required number of men becomes:

    [tex]n \times 12 \text{ hours/day} \times 20 \text{ days} = 24,000 \text{ man-hours}[/tex]

    Solving for [tex]n[/tex], we have:

    [tex]n \times 240 = 24,000[/tex]

    [tex]n = \frac{24,000}{240}[/tex]

    [tex]n = 100[/tex]

Therefore, 100 men are required to complete the work in 20 days working 12 hours per day.

The correct answer is [tex]\boxed{A}[/tex] 100.