Final answer:
To determine how many more men are needed to complete the work in 15 days, calculate the total work in man-days (18 men * 45 days) and then divide by the new time frame (15 days) to find the new total number of men required (54 men). Subtract the original number of men (18 men) to find the additional men needed, which is 36 men.
Step-by-step explanation:
If 18 men can complete a piece of work in 45 days, to find how many more men should be employed to complete the work in 15 days, we can use the concept of work done which involves man-days. A "man-day" is a measure of work completed by one person in a single day. In this case, the total work to be done can be described in man-days as the product of the number of men and the days they work.
Total man-days required for the work = 18 men × 45 days = 810 man-days
Now, if we want to complete the same work in 15 days, we divide the total man-days by the number of days to get the required number of men:
Required number of men = 810 man-days ÷ 15 days = 54 men
Since we already have 18 men, the number of additional men needed is:
Additional men = 54 men - 18 men = 36 men
Therefore, 36 more men should be employed to complete the work in 15 days.