Twenty men complete one third of a job in 20 days. How many additional men must be employed so that the remaining two thirds of the job is finished in 25 more days?

Introduction / Context:
Time and work problems often assume constant individual productivity. Total work equals rate times time. When more workers are added, the group rate scales linearly with the number of workers, assuming identical efficiency.

Given Data / Assumptions:

• 20 men do 1/3 of the job in 20 days.
• Remaining work is 2/3 of the job.
• Goal: finish the remaining 2/3 in 25 days with a larger team.

Concept / Approach:
Let r be the daily work of one man. Work done = men * r * days. First use the first phase to compute r, then determine how many men are needed for the second phase, and finally compute how many extra men must be added to the initial 20.

Step-by-Step Solution:

Verification / Alternative check:
With 32 men for 25 days, total work = 32 * (1/1200) * 25 = 2/3, which exactly meets the remaining requirement.

Why Other Options Are Wrong:

• 15, 18, 25, 10 give total men ≠ 32, leading to over or under completion.

Common Pitfalls:
Subtracting men instead of adding; calculating total men as the answer rather than the number of additional men; mixing up 1/3 and 2/3 portions.

Final Answer:
12