Manpower adjustment on a fixed deadline: A contractor plans to finish a job in 40 days. He employs 100 men initially and adds 100 more after 35 days, finishing on time. If he had not added extra men, how many days late would the work be?

Introduction / Context:
This is a work–time problem converting varying workforce over time into total man-days. Once the total man-days for completion are known, we can compute the time if only the original crew worked throughout and compare with the target to find the delay.

Given Data / Assumptions:

• Target duration = 40 days.
• First 35 days: 100 men.
• Last 5 days: 200 men (100 original + 100 additional).
• Uniform productivity; man-days add linearly.

Concept / Approach:
Total work W equals the sum of man-days used in the actual schedule. Then compute how long 100 men alone would take: time_alone = W / 100. The delay = time_alone − 40, if positive.

Step-by-Step Solution:

Verification / Alternative check:
Check proportionality: replacing the final 5 days of 100 men with 200 men adds 500 extra man-days, exactly the shortfall that would have caused a 5-day delay at 100 man-days/day.

Why Other Options Are Wrong:

• 7, 12, 18: Do not match the precise calculation showing a 5-day delay.
• None: Correct here because 5 is not listed among the numerical choices.

Common Pitfalls:
Forgetting that “additional 100 men” means total 200 in the last 5 days, or miscomputing total man-days. Always aggregate man-days and then divide by the constant crew size for alternative schedules.

Final Answer: