Final answer:
The number of men required to dig 8 hectares in 12 days, when 18 men can dig 6 hectares in 15 days, is calculated by setting up a proportion of work done. The solution to the proportion gives us the answer of 16.875 men, which means 17 men are needed when rounding to a whole person.
Step-by-step explanation:
The question asks us to determine the number of men required to dig 8 hectares of land in 12 days, given that 18 men can dig 6 hectares in 15 days. This is a problem of direct proportion where we can use the concept of work to solve it. The work done by a certain number of workers in a given time is constant, and we set up a proportion based on the data provided.
The formula for work done (W) is W = number of men (M) × number of days (D) × area of land (A). From the question, we have for the first scenario, W1 = 18 men × 15 days × 6 hectares. For the second scenario, we are to find the number of men required (M2), so W2 = M2 × 12 days × 8 hectares.
Since the work done in both scenarios is equal (W1 = W2), we have 18 × 15 × 6 = M2 × 12 × 8. Simplifying this equation will give us the value of M2, which is the number of men needed. M2 can be calculated as follows:
M2 × 12 × 8 = 18 × 15 × 6
M2 = (18 × 15 × 6) / (12 × 8)
M2 = (18 × 15 × 6) / 96
M2 = 16.875
Since we cannot have a fraction of a man, we would need 17 men to dig 8 hectares in 12 days.