Twenty four men can complete a job in 16 days, while thirty six women can complete the same job in 24 days. In how many days will 8 men and 6 women together complete the job?

Introduction / Context:
Different categories of workers have different per person rates. We extract each category’s per person daily rate from the given completions and then add them for the mixed group.

Given Data / Assumptions:

• 24 men finish in 16 days.
• 36 women finish in 24 days.
• Find completion time for 8 men and 6 women together.

Concept / Approach:
Compute 1 man per day rate and 1 woman per day rate from the team completions, then compute the mixed rate and take the reciprocal to get time.

Step-by-Step Solution:

Verification / Alternative check:
Convert women to man equivalents: 1 woman = 4/9 man, then 8 men + 6 women = 8 + 6*(4/9) = 8 + 8/3 = 32/3 men; time = (24 men * 16 days) / (32/3) ≈ 36 days, consistent.

Why Other Options Are Wrong:
28, 32, 24, 30 correspond to incorrect rate conversions or algebraic slips while combining categories.

Common Pitfalls:
Assuming men and women have the same per person rate; adding days instead of rates; arithmetic errors with 384 and 864 denominators.

Final Answer:
36 days