A alone can complete a job in 12 days and B alone in 24 days. Working together, in how many days can they complete the job?

Introduction / Context:
When two workers collaborate, the combined rate is the sum of individual rates. The completion time is the reciprocal of the combined rate for a unit job.

Given Data / Assumptions:

• A: 12 days ⇒ 1/12 per day.
• B: 24 days ⇒ 1/24 per day.

Concept / Approach:
Sum the rates and invert to get time.

Step-by-Step Solution:

Verification / Alternative check:
In 8 days, A produces 8/12 = 2/3 and B produces 8/24 = 1/3. Total equals 1 job, confirming the result.

Why Other Options Are Wrong:
6 and 4 underestimate the time; 10 and 12 overestimate; only 8 days matches the real sum of rates.

Common Pitfalls:
Averaging times instead of summing rates; arithmetic slips with fractions 1/12 and 1/24.

Final Answer:
8 days