A contractor planned to finish a project in 60 days. After 20 days, only one-fifth (1/5) of the work was completed with 75 workers employed. To finish on time, how many additional workers are required for the remaining 40 days (assume output is proportional to workforce)?

Introduction / Context:
This is a workforce planning question. If progress lags behind schedule, we can scale workforce proportionally to required daily completion rates to meet the deadline.

Given Data / Assumptions:

• Total target duration = 60 days.
• After 20 days, completed = 1/5 of work (20%).
• Initial workforce = 75 workers.
• Output is proportional to the number of workers.

Concept / Approach:
Compute current daily completion rate and the required daily rate for the remaining period. The ratio of required to current rate gives the factor by which the workforce must be increased.

Step-by-Step Solution:
Current progress: 1/5 in 20 days ⇒ current rate = (1/5)/20 = 1/100 per day. Remaining work = 4/5; remaining time = 40 days. Required rate = (4/5)/40 = 1/50 per day. Factor needed = (required rate) / (current rate) = (1/50) / (1/100) = 2. Therefore, workforce must double from 75 to 150. Additional workers = 150 − 75 = 75.

Verification / Alternative check:
With 150 workers at twice the initial rate, 1/50 per day * 40 days = 4/5, perfectly matching the remaining work.

Why Other Options Are Wrong:
25 or 50 insufficient; “can’t be determined” is incorrect because proportionality is given; 30 is arbitrary.

Common Pitfalls:
Comparing elapsed time to completed fraction without computing daily rates; forgetting to scale workforce based on required daily completion rate.

Final Answer:
75