Work proportionality (similar wall): 8 persons build a 140 m wall in 42 days. In how many days can 30 persons build a similar wall of length 100 m?

Introduction / Context:
When work is directly proportional to length, and productivity is constant per person per day, the required days scale with wall length and inversely with workforce size. Convert the first scenario into person-days per meter to answer the second scenario quickly.

Given Data / Assumptions:

• 8 persons build 140 m in 42 days.
• Find days for 30 persons to build 100 m of a similar wall.

Concept / Approach:
Person-days per meter = (persons * days) / length. Multiply by target length to get total person-days needed, then divide by the new number of persons to get days.

Step-by-Step Solution:

Verification / Alternative check:
Proportionality: Time ∝ length / persons ⇒ T2 = T1 * (100/140) * (8/30) * (persons/?) after re-arranging yields the same numeric result when applied carefully.

Why Other Options Are Wrong:
11, 13, 19, 10 days do not match the calculated 240 person-days divided by 30 persons.

Common Pitfalls:
Forgetting to scale by both length and workforce, or mixing days and persons in the proportion incorrectly.

Final Answer:
8 days