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Question 784618: A group of men decided to do a job in 4days. but since 20 men dropped out everyday, the job completed at the end of the 7th day. How many men were there at the beginning?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let n = the number of men at the beginning
The rate of work = 1 job/4 days/n men
Assuming the first group of 20 did not drop out until the end of the first day, n men worked the first day.
So after the 1st day, 1/4 of the job was complete
On the 2nd day n-20 men completed (1/4n)*(n-20) of the job
On the 3rd day n-40 men completed (1/4n)*(n-40) of the job, and so on.
After 7 days, the entire job is complete, so we can sum up all the fractions of the job done on each day and set them equal to 1:
1 = 1/4 + (n-20)/4n + (n-40)/4n + (n-60)/4n + (n-80)/4n + (n-100)/4n + (n-120)/4n
3/4 = (6n - 420)/4n
Solve for n:
12n = 24n - 1680
12n = 1680
n = 140
So there were 140 men at beginning
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