Inverse proportionality with number of workers: 6 boys can complete a job in 16 hours. Assuming equal productivity for each boy, in how many hours will 8 boys complete the same job?

Introduction / Context:
When more identical workers are added, the time decreases inversely with the number of workers, provided productivity per worker remains the same and there are no constraints like crowding or setup times.

Given Data / Assumptions:

• 6 boys finish in 16 hours.
• All boys have equal constant productivity.
• We need the time with 8 boys.

Concept / Approach:
Total work W is fixed. Work = (number of boys) * (hours). Therefore, time for 8 boys = (6 * 16) / 8 hours.

Step-by-Step Solution:
W = 6 * 16 = 96 boy-hours.With 8 boys, time = 96 / 8 = 12 hours.

Verification / Alternative check:
Proportional check: Going from 6 to 8 workers is a factor of 6/8 = 0.75 in time. 0.75 * 16 = 12 hours, consistent.

Why Other Options Are Wrong:

• 10, 8, 14 do not match the invariant W = 96 boy-hours with 8 workers.

Common Pitfalls:

• Assuming time decreases linearly with an absolute difference in workers (it is inverse proportional, not additive).

Final Answer:
12