If 8 men can reap 80 hectares of a field in 24 days, then how many hectares can 36 men reap in 30 days at the same rate of working?

Introduction / Context:
This is a classic work and chain rule question where both the number of workers and the time change, and you are asked to find the new quantity of work done. The scenario is framed in terms of men reaping hectares, but the underlying logic is about proportionality among men, days and total work.

Given Data / Assumptions:

• 8 men reap 80 hectares in 24 days.
• All men work at the same constant rate.
• The number of men increases to 36.
• The number of days is 30.
• We need to find how many hectares can be reaped in this new situation.

Concept / Approach:
Total work done is proportional to the product of number of men, number of days and the per man per day rate. From the first situation, we can compute the rate in hectares per man per day. Then we multiply this rate by the new number of men and new number of days to get the total area that can be reaped.

Step-by-Step Solution:
Step 1: Compute total man days in the first case: 8 men * 24 days = 192 man days.Step 2: These 192 man days produce 80 hectares.Step 3: Rate of work per man per day = 80 / 192 hectares.Step 4: In the new case, we have 36 men and 30 days, so man days = 36 * 30 = 1080.Step 5: Total area reaped = 1080 * (80 / 192) hectares.Step 6: Simplify: 1080 / 192 = 5.625, and 5.625 * 80 = 450 hectares.

Verification / Alternative check:
Use proportional reasoning directly. When we change from 8 men to 36 men, the workforce is multiplied by 36 / 8 = 4.5. The time increases from 24 days to 30 days, a factor of 30 / 24 = 1.25. Combined factor = 4.5 * 1.25 = 5.625. Multiply the original 80 hectares by 5.625 to obtain 450 hectares, which matches the detailed calculation.

Why Other Options Are Wrong:
350, 400 or 425 hectares all assume a smaller combined growth factor than the correct value 5.625. 500 hectares would require a higher factor and thus overestimates the productivity of the new team and duration.

Common Pitfalls:

• Forgetting to change both men and days together, and adjusting for only one of them.
• Using an incorrect ratio like 8 / 36 instead of 36 / 8, which inverts the effect.
• Doing arithmetic with large numbers without simplification, leading to calculation errors.

Final Answer:
The 36 men can reap 450 hectares in 30 days.