If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days, assuming the work rate per man remains constant?

Introduction / Context:
This is a standard work and manpower question where the total work done depends on the number of workers and the number of days they work, assuming a constant rate of work per person. Such problems commonly appear in aptitude tests to check understanding of direct proportionality between workers, time and work done.

Given Data / Assumptions:
• 12 men can reap 120 acres of land in 36 days.
• We must find how many acres 54 men can reap in 54 days.
• Each man works at a constant rate throughout the period.
• Work done is directly proportional to (number of men) * (number of days).

Concept / Approach:
Total work can be expressed in man-days and then converted to actual acres using proportionality. First find how many acres are done per man-day. Then, compute the total man-days in the second scenario and multiply by the per man-day rate to get the number of acres reaped by 54 men in 54 days.

Step-by-Step Solution:
Step 1: In the first situation, total man-days = 12 men * 36 days = 432 man-days.Step 2: These 432 man-days correspond to 120 acres, so each man-day covers 120 / 432 acres.Step 3: Simplify 120 / 432 = 5 / 18. So one man-day reaps 5/18 acres.Step 4: In the second situation, total man-days = 54 men * 54 days = 2916 man-days.Step 5: Acres reaped = man-days * acres per man-day = 2916 * (5 / 18).Step 6: Compute 2916 / 18 = 162, then multiply 162 * 5 = 810 acres.

Verification / Alternative check:
We can also use proportionality directly: the number of men increases from 12 to 54 (factor 54 / 12 = 4.5), and days increase from 36 to 54 (factor 54 / 36 = 1.5). Total work is multiplied by 4.5 * 1.5 = 6.75. So new acres = 120 * 6.75 = 810 acres, confirming the earlier calculation.

Why Other Options Are Wrong:
710 acres and 760 acres are both too small; they correspond to lower effective work rates than given by the original data.
860 acres is larger than 810 acres and does not match any integer multiple of the base scenario when proportional factors are correctly computed. Only 810 acres is consistent with the given numbers.

Common Pitfalls:
A common mistake is to scale only by men or only by days, instead of taking both changes into account. Another error is to miscalculate the per man-day rate by dividing incorrectly or not simplifying the fraction properly. Always compute total man-days first, then apply the rate logically.

Final Answer:
The 54 men can reap 810 acres of land in 54 days.