Twenty four boys can complete a job in 12 days, while sixteen men can complete the same job in 9 days. In how many days can 12 boys and 12 men together complete the job?

Introduction / Context:
This problem compares two worker types. We equate the total work from each scenario to relate one man’s productivity to one boy’s productivity, then compute the combined team rate.

Given Data / Assumptions:

• 24 boys finish in 12 days.
• 16 men finish in 9 days.
• Find time for 12 boys and 12 men together.

Concept / Approach:
Let 1 boy per day produce b units, 1 man per day produce m units, and let total work be W. From each scenario, write W in terms of b and m to find m in terms of b. Then add rates for the mixed team and compute time = W / rate.

Step-by-Step Solution:

Verification / Alternative check:
Using man boy equivalence 1 man = 2 boys, the mixed team equals 12 + 24 = 36 boy equivalents, and 288 boy days / 36 equals 8 days.

Why Other Options Are Wrong:
6, 7, 10, 9 assume the wrong boy to man equivalence or misdivide total boy days by the combined equivalent rate.

Common Pitfalls:
Adding times rather than rates; treating men and boys as identical; miscomputing the equivalence ratio from the two full team cases.

Final Answer:
8 days