Relative efficiency and combined time: A is twice as efficient as B (i.e., A’s daily work rate is 2 times B’s). Together they finish a job in 14 days. In how many days can A alone finish the job?

Introduction / Context:
This problem uses efficiency ratios. If A is twice as efficient as B, then A and B’s rates are in the ratio 2:1. The combined rate and total time are given, allowing us to isolate A’s time.

Given Data / Assumptions:

• A : B (rates) = 2 : 1.
• Together they complete the job in 14 days.

Concept / Approach:
Let B’s rate be r; then A’s rate is 2r. Combined rate is 3r. If one full job requires time T with combined rate, then T = 1 / (3r). Since T = 14, we get r and then A’s time = 1 / (2r).

Step-by-Step Solution:
3r = 1/14 ⇒ r = 1/42A’s rate = 2r = 2/42 = 1/21A’s time alone = 1 / (1/21) = 21 days

Verification / Alternative check:
Check: A+B combined rate = 1/21 + 1/42 = 3/42 = 1/14, so 14 days is consistent.

Why Other Options Are Wrong:

• 18, 20, 24 are not consistent with the 2:1 efficiency ratio and 14-day combined time.

Common Pitfalls:

• Using time ratios directly (they are inverse of efficiency ratios).

Final Answer:
21