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?

Difficulty: Easy

36 days
24 days
18 days
12 days
None of these

Correct Answer: 36 days

Explanation:

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:

Let B’s rate = bA’s rate = 2bTogether: 2b + b = 3b = 1/12 ⇒ b = 1/36Therefore, B alone takes 1 / b = 36 days

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.

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?

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