Proportional workforce scaling: If 3 men and 4 boys can complete a piece of work in 8 days, then how many days are required for 6 men and 8 boys to complete the same work (assume same individual efficiencies)?

Introduction / Context:
When the entire workforce is doubled (both men and boys in the same proportions), and all efficiencies are constant, the time required halves. This uses the linearity of work with respect to total effective workers and time.

Given Data / Assumptions:

• (3 men + 4 boys) finish in 8 days.
• (6 men + 8 boys) is exactly double the effective workforce.
• Efficiencies are constant; work remains the same 1 job.

Concept / Approach:
Work = (effective workers) * days. Doubling workers halves the required days for the same work.

Step-by-Step Solution:
Original man-equivalents: W = (3M + 4B) * 8. New team is 2*(3M + 4B), so days = 8 / 2 = 4.

Verification / Alternative check:
If you define rates m and b, original daily rate = 3m + 4b; doubled rate = 6m + 8b = 2*(3m + 4b); the time divides by 2.

Why Other Options Are Wrong:
2 days would require a quadrupling, not doubling. 6 and 16 days contradict proportionality.

Common Pitfalls:
Changing only men or only boys in comparisons; here both categories are doubled, preserving ratio.

Final Answer:
4 days