Inverse men–days relation: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work (same rate)?

Introduction / Context:
With constant productivity, work done equals men * days. For a fixed job, men and days are inversely proportional. Reducing workers increases the required days proportionally.

Given Data / Assumptions:

• 36 men finish in 18 days.
• Find days for 27 men at same rate.

Concept / Approach:
Use men1 * days1 = men2 * days2. Solve for days2 with the given numbers.

Step-by-Step Solution:

Verification / Alternative check:
Total man-days = 36 * 18 = 648. With 27 men, days = 648 / 27 = 24. Same result.

Why Other Options Are Wrong:

• 23, 34, 39: Do not preserve the constant man-days 648 for the fixed job.

Common Pitfalls:
Using direct instead of inverse proportion between men and days for fixed work. Keep the product men * days constant for the given job.

Final Answer: