A contractor undertakes to complete a piece of work in 120 days and initially employs 140 men on the job. At the end of 66 days it is found that only half of the work has been completed, so the contractor hires 25 extra men. By how many days does the actual completion time exceed the originally specified period of 120 days?

Introduction / Context:
This problem involves a contractor who has underestimated the workforce needed to complete a job on time. The question tests understanding of work rate, total work in man days, and how adding more workers affects completion time. We are asked to determine by how many days the actual completion exceeds the originally agreed schedule.

Given Data / Assumptions:

• Planned schedule: the job should be completed in 120 days with 140 men.
• After 66 days, only half of the work is complete.
• From day 67 onward, 25 additional men are employed, so total workers become 165.
• All men work at the same constant rate and work full days.

Concept / Approach:
The key is to treat the work rate as men days. Half of the total work is completed in 66 days by 140 men. That allows us to compute the total work in men days. Knowing how much work remains and the new workforce size, we compute the remaining time required. Adding this to the initial 66 days gives the actual total duration, which we compare to the originally planned 120 days.

Step-by-Step Solution:
Let the total work be W men days. Given that half the work is completed in 66 days by 140 men, we have W / 2 = 140 * 66. Therefore, W = 2 * 140 * 66 = 140 * 132 = 18480 men days. Remaining work after 66 days is W / 2 = 18480 / 2 = 9240 men days. After hiring extra men, total workers = 140 + 25 = 165 men. Time to complete the remaining work = 9240 / 165 days. Simplify 9240 / 165 = 56 days. So, actual total time taken = 66 days + 56 days = 122 days. Excess time beyond the specified 120 days = 122 - 120 = 2 days.

Verification / Alternative check:
Compute the effective average workforce if the entire 18480 men days of work are spread over 122 days: 18480 / 122 is approximately 151.5 men. The actual schedule uses 140 men for 66 days and 165 men for 56 days, which averages out to this value. This shows the calculation is consistent and the total men days tally correctly with the work done.

Why Other Options Are Wrong:
3 days would correspond to an actual duration of 123 days, which would require a slightly different remaining work or strength, not supported by the given data. 4 days or 5 days excess time would imply 124 or 125 days total, which would contradict the computed remaining time of 56 days with 165 men. 1 day extra (121 days total) is too small and would not allow enough time for 165 men to complete the remaining 9240 men days of work.

Common Pitfalls:
A common mistake is to assume that the initial plan 140 men * 120 days equals the actual total work, even though the progress data shows that only half the work was done in 66 days. The actual total work must be recalculated from the given progress information. Another trap is arithmetic simplification errors while dividing 9240 by 165. Carefully factor both numbers or use cancellation to avoid mistakes.

Final Answer:
The contractor exceeds the specified time by 2 days.