Relative efficiencies from joint completion time A and B can complete a job together in 12 days. A is exactly 2 times as efficient as B. In how many days can B alone complete the job?

Introduction / Context:This problem leverages the ratio of efficiencies. If A is 2 times as efficient as B, A’s rate is double B’s rate. From the joint time we can extract each individual time.

Given Data / Assumptions:

• A is 2x as efficient as B.
• Together they finish in 12 days.
• Total work normalized to 1.

Concept / Approach:If B’s rate is b, A’s rate is 2b. Together rate = 3b = 1/12 ⇒ b = 1/36.

Step-by-Step Solution:

Verification / Alternative check:Check rates: A = 2/36 = 1/18; B = 1/36; Together = 1/18 + 1/36 = 3/36 = 1/12.

Why Other Options Are Wrong:24, 18, 12 are not consistent with the 3b = 1/12 relationship.

Common Pitfalls:Confusing “2 times as efficient” with “2 days less” or miscomputing sum of rates.

Final Answer:36 days