Sixteen children and twenty-four men can finish a job in 18 days. If each child takes twice as long as each man to do the job alone (i.e., a child is half as efficient as a man), in how many days will 24 men finish the same job?

Introduction / Context:The statement that a child takes twice the time a man takes implies each child's daily rate is half that of a man. Use equivalent-man units to compute the team's rate and then the time for 24 men alone.

Given Data / Assumptions:

• 16 children + 24 men finish in 18 days.
• Child = 1/2 man in efficiency.

Concept / Approach:Convert children to man-equivalents, compute total daily man-equivalents, find job size in man-days, then divide by 24 men.

Step-by-Step Solution:

Verification / Alternative check:Proportional scaling with equivalent units yields an integer result, indicating internal consistency.

Why Other Options Are Wrong:They represent incorrect conversions or divisions when moving between mixed crews and a men-only crew.

Common Pitfalls:Misreading the phrase “twice the time” as “twice as efficient”; always convert carefully.

Final Answer:24 days