if 8 men can do a job in days, what is the percentage increase in number of days required to do the job when 2 men are released?
not just an answer please.
A.16 2/3%
B.25%
C. 33 1/3%
D.40%
E.48%
6 men is 3/4 of 8 men
So, they can only do 3/4 as much work in a day.
So, it takes 4/3 as many days, or
(C)
suppose it took n days
number of man-days = 8n
if done by 6 men
number of days = 8n/6 = 4n/3
change in days = 4n/3 - n = (1/3)n
percentage change = (1/3)n / n = 1/3 or 33 1/3%
To solve this problem, let's break down the steps:
1. Determine the number of days it takes for 8 men to complete the job. Let's call this number "x".
2. Determine the number of days it would take for 6 men to complete the job. Since 2 men were released, there are now 6 men. Let's call this number "y".
3. Calculate the percentage increase in days required to do the job when 2 men are released using the formula:
((y - x) / x) * 100.
Now let's calculate each step:
1. If 8 men can complete the job in x days, the rate at which they work is 1 job per x days per man. Therefore, 8 men can complete 8/x of the job in one day.
2. If 6 men are tasked with completing the job, they still work at the same rate of 1 job per man per x days. Therefore, 6 men can complete 6/x of the job in one day.
3. We need to calculate the percentage increase between y and x:
((6/x - 8/x) / (8/x)) * 100.
Simplifying, we get:
((-2/x) / (8/x)) * 100.
Dividing both the numerator and the denominator by x gives us:
(((-2) / 8) * 100) / x.
Since x represents the original number of days required, we don't need its specific value to find the percentage increase. Therefore, the answer is independent of the value of x.
Now let's calculate the final result:
((-2) / 8) * 100 = -25.
Therefore, the percentage increase is -25%.
However, negative percentages are not commonly used to express increases. We need to convert this to a positive percentage by taking the absolute value:
|-25| = 25.
The final answer is 25%, which corresponds to option B.
To determine the percentage increase in the number of days required to do the job when 2 men are released, we need to compare the new number of days to the initial number of days.
Let's start by determining the initial number of days. If 8 men can do the job, we can say that it takes 1 man 8 times longer to complete the job alone. Therefore, 1 man can complete the job in 8 days.
Next, let's calculate the new number of days required to complete the job after 2 men are released. If 2 men are released, that means only 6 men are left to do the job. To find out how many days it will take them, we can express it as a ratio:
8 men take 1 day
6 men will take x days
Using the concept of inverse variation, we can set up the equation:
8 * 1 = 6 * x
Solving for x, we get:
8 = 6x
x = 8/6
x = 4/3
So, when 2 men are released, it will take the remaining 6 men 4/3 of a day to complete the job.
Now, let's calculate the percentage increase in the number of days. We can find the difference between the initial and new number of days, and then express it as a percentage of the initial number of days:
Difference = new number of days - initial number of days
Difference = (4/3) - 1
Difference = 1/3
Percentage increase = (Difference / initial number of days) * 100
Percentage increase = (1/3) / 1 * 100
Percentage increase = (1/3) * 100
Percentage increase = 100/3
Percentage increase = 33 1/3%
Therefore, the percentage increase in the number of days required to do the job when 2 men are released is 33 1/3%. So, the correct answer is C. 33 1/3%.