Final answer:
The original question regarding how many men must be discharged at the end of the 18th day contains a discrepancy, as calculations show that 176 men are needed in the remaining 5 days to complete the work, indicating a need for additional men rather than a reduction.
Step-by-step explanation:
The question asks us to solve a work-time problem involving the number of men and the days required to complete a task. To begin, let's establish the work rate for the original 100 men.
Since they complete one third of the work in 10 days, they will complete the full work in 30 days. Now, starting on the eleventh day, 160 men (100 original + 60 additional) will be working, hence increasing the total work rate.
We can address the problem by calculating the collective number of man-days required to finish the entire job. The first 10 days account for 1000 man-days (100 men x 10 days). Since the entire work is equivalent to 3000 man-days (100 men x 30 days), there are 2000 man-days of work left after the first 10 days.
Over the next 7 days, 160 men work, which gives an additional 1120 man-days (160 men x 7 days), leaving 880 man-days of work to be completed in the remaining 5 days. To find out how many men are required, we divide the remaining man-days by the remaining days: 880 man-days ÷ 5 days = 176 men.
Therefore, at the end of the 18th day, the number of men working needs to be reduced to 176 from 160. Since you can't have negative dismissals, it indicates that no men need to be discharged and instead, additional men might be necessary.
There seems to be an error in the phrasing of the question or in our interpretation. If the problem is correctly stated, and assuming all men work at the same rate, the calculation would imply that no men should be discharged, and the number of men must in fact be increased to meet the deadline.