A is twice as efficient as B, and together they finish a job in 14 days. In how many days can A alone finish the job?

Introduction / Context:
Relative efficiency problems can be handled by assigning a variable to one worker’s rate and expressing the other’s rate as a multiple. Sum the rates to meet the joint time.

Given Data / Assumptions:

• A is twice as efficient as B ⇒ rate of A = 2b if rate of B = b.
• Together they take 14 days ⇒ combined rate = 1/14.

Concept / Approach:
Set B rate to b, then A rate is 2b. Add to get 3b and equate to 1/14 to solve for b, then compute A’s time as 1 divided by A’s rate.

Step-by-Step Solution:

Verification / Alternative check:
Check combined: 1/21 + 1/42 = 3/42 = 1/14, consistent with the given joint time.

Why Other Options Are Wrong:
11, 28, 42, 14 do not satisfy the joint time when combined with B’s rate and the 2:1 efficiency relation.

Common Pitfalls:
Misreading twice as efficient; averaging times instead of rates; arithmetic slips with fractional rates.

Final Answer:
21 days