Mixed workforce rates: 8 men finish the job in 12 days; 4 women finish it in 48 days; 10 children finish it in 24 days. In how many days will 10 men, 4 women, and 10 children working together complete the same job?

Introduction / Context:Different categories of workers often have different speeds. Convert each category to a per-person daily rate, add rates to get a team rate, and then compute time = work / rate. The unitary-method approach keeps the arithmetic clean and scalable.

Given Data / Assumptions:

• 8 men complete in 12 days ⇒ 1 man's rate = 1 / (8*12) = 1/96 job/day.
• 4 women complete in 48 days ⇒ 1 woman's rate = 1 / (4*48) = 1/192 job/day.
• 10 children complete in 24 days ⇒ 1 child's rate = 1 / (10*24) = 1/240 job/day.
• Team: 10 men + 4 women + 10 children.

Concept / Approach:Team rate = sum of individual rates, then time = 1 / (team rate). Be precise with fractions to avoid compounding rounding errors.

Step-by-Step Solution:

Verification / Alternative check:Since the combined rate is exactly 1/6 job/day, finishing in 6 days is exact (no rounding).

Why Other Options Are Wrong:5, 7, 8, 10 days contradict the exact combined-rate computation 1/6 job/day.

Common Pitfalls:Adding times instead of rates, or using proportional reasoning on days rather than on daily work rates leads to wrong results.

Final Answer:6 days