Thirty men take 20 days to complete a job working 9 hours a day.How many hour a day should 40 men work to complete the job?
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8 hrs
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7 1/2 hrs
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7 hrs
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9 hrs
Total work = 30 men × 20 days × 9 hours = 5400 man-hours. With 40 men: 5400/40 = 135 days total. Hours per day = 5400/(40×20) = 7.5 hours. The inverse proportion between men and hours (when days are constant) gives: (30×9)/40 = 7.5 hours per day.
To solve this problem, we can use the concept of man-hours.
Given that 30 men can complete the job in 20 days, working 9 hours a day, we can calculate the total man-hours required to complete the job.
Total man-hours = (Number of men) x (Number of days) x (Number of hours per day) Total man-hours = 30 men x 20 days x 9 hours/day Total man-hours = 5400 man-hours
Now, let's determine how many hours a day 40 men should work to complete the job.
Total man-hours = (Number of men) x (Number of days) x (Number of hours per day) 5400 man-hours = 40 men x (Number of days) x (Number of hours per day)
We need to solve for the number of hours per day. Let's rearrange the equation:
(Number of days) x (Number of hours per day) = 5400 man-hours / 40 men (Number of days) x (Number of hours per day) = 135 man-hours
Since we want to find the number of hours per day, we can divide both sides of the equation by the number of days:
(Number of hours per day) = 135 man-hours / (Number of days)
Substituting the given number of days (20) into the equation:
(Number of hours per day) = 135 man-hours / 20 days (Number of hours per day) = 6.75 hours/day
Therefore, 40 men should work 6.75 hours a day to complete the job.
Among the given options: A) 8 hrs B) 7 1/2 hrs C) 7 hrs D) 9 hrs
The correct answer is B) 7 1/2 hrs, which is equivalent to 7.5 hours.