Question 784618
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