24 men works for 14 days, 2 days after they started working, 4 more men joined them and after 2 more days, 6 men left. How many more days will they now take to complete the remaining work?
So, the total man-days worked in the 14 days is
2*24 + 2*28 + 10*22 = 324
Without knowing how much total work is needed, there's no way to tell how many more days it will take.
To find out how many more days it will take to complete the remaining work, we need to calculate the total amount of work done by the initial 24 men in the first 2 days, then the work done by the additional 4 men in the next 2 days, and finally subtract the work undone by the 6 men who left.
Let's calculate the work done by 24 men in 2 days:
Work done by 1 man in 1 day = 1/14 (since 24 men work for 14 days)
Work done by 1 man in 2 days = 1/14 x 2 = 1/7
Work done by 24 men in 2 days = (1/7) x 24 = 24/7
Now let's calculate the work done by the additional 4 men in 2 days:
Work done by 1 man in 1 day = 1/14 (since 24 men work for 14 days)
Work done by 1 man in 2 days = 1/14 x 2 = 1/7
Work done by 4 men in 2 days = (1/7) x 4 = 4/7
Now subtract the work undone by the 6 men who left:
Work undone by 1 man in 1 day = 1/14 (since 24 men work for 14 days)
Work undone by 1 man in 2 days = 1/14 x 2 = 1/7
Work undone by 6 men in 2 days = (1/7) x 6 = 6/7
Net work done in the first 4 days: (24/7) + (4/7) - (6/7) = (24 + 4 - 6)/7 = 22/7
Since the remaining work is the total work minus the net work done in the first 4 days, we subtract 22/7 from 1 to get the fraction of remaining work.
Fraction of remaining work = 1 - 22/7 = (7 - 22)/7 = -15/7
Since the fraction of remaining work is negative, it means that the work has already been completed. Therefore, no more days are needed to complete the remaining work.
In conclusion, no more days are needed to complete the remaining work as it has already been finished.