Twenty persons complete one-third (1/3) of a job in 12 days. How many additional persons are needed to complete the remaining work in the next 12 days (assume equal efficiency)?

Introduction / Context:
This is a standard manpower scaling question: if a certain team completes a fraction in a certain time, we determine how many workers are necessary to complete the remainder in a specified time, assuming uniform efficiencies.

Given Data / Assumptions:

• 20 persons complete 1/3 of work in 12 days.
• Remaining work = 2/3.
• Desired remaining duration = 12 days.
• Worker efficiencies are equal and constant.

Concept / Approach:
Compute one person’s daily work rate from the first phase. Use it to find the total number of persons required for the second phase. Subtract existing 20 to get “additional” persons required.

Step-by-Step Solution:
Let r = one person’s daily work. From first phase: 20 * r * 12 = 1/3 ⇒ r = 1 / 720. For remaining 2/3 in 12 days with N persons: N * r * 12 = 2/3. Substitute r: N * (1/720) * 12 = 2/3 ⇒ N / 60 = 2/3 ⇒ N = 40. Additional persons needed = 40 − 20 = 20.

Verification / Alternative check:
With 40 persons: 40 * (1/720) * 12 = 2/3 as required.

Why Other Options Are Wrong:
12, 15, 18, 40 do not reflect the “additional” headcount computed; 40 is the total requirement, not the increment.

Common Pitfalls:
Confusing total required with extra required; not deriving the per-person rate first.

Final Answer:
20