Three men or four women can build a wall in 43 days. In how many days can seven men and five women build the same wall?

Introduction / Context:
This is a combined workforce problem with different worker categories. We convert each category to a consistent daily rate and then add rates for mixed teams.

Given Data / Assumptions:

• 3 men complete 1 wall in 43 days.
• 4 women complete 1 wall in 43 days.
• Find days for 7 men and 5 women together.

Concept / Approach:
Compute the per person daily rate for men and women using the equivalences given. Sum the rates for the mixed team, then take the reciprocal to get the time to complete 1 wall.

Step-by-Step Solution:

Verification / Alternative check:
Proportions are consistent with the given single category completions. The exact fractional arithmetic yields a clean 1/12 rate, confirming 12 days.

Why Other Options Are Wrong:
16, 25, 21, 18 days correspond to incorrect rate sums or arithmetic slips when converting single category times to per person rates.

Common Pitfalls:
Assuming 1 man equals 1 woman; ignoring that both categories have different per person rates; averaging days instead of adding rates.

Final Answer:
12 days