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.
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]
Determine New Work Conditions:
Now, we want this same work to be completed in 20 days, by working 12 hours each day.
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.
