A takes twice as long as B to finish a job, and C takes three times as long as B. Working together, they finish the job in 12 days. How many days would A take to do the job alone?

Introduction / Context:
Express all times relative to B. Convert to rates, add to get the joint rate, equate to the given joint time, and back out A’s time.

Given Data / Assumptions:

• A = 2B, C = 3B (in time).
• Together time = 12 days.

Concept / Approach:
If B needs t days, then rates are: A = 1/(2t), B = 1/t, C = 1/(3t). Sum to get 11/(6t). Set 12 * 11/(6t) = 1 to solve for t and then 2t.

Step-by-Step Solution:

Verification / Alternative check:
Compute joint rate with t=22: 1/44 + 1/22 + 1/66 = 1/12 → consistent.

Why Other Options Are Wrong:
They correspond to incorrect algebra when resolving t or doubling to get A’s time.

Common Pitfalls:
Adding times rather than rates; mixing up “takes twice the time” with “twice as efficient.”

Final Answer:
44