A can complete a piece of work in 12 days. Worker B is 60% more efficient than A. In how many days will B alone complete the same work at this higher efficiency?

Introduction / Context:
This is a straightforward time and work problem comparing efficiencies. Worker A completes a job alone in a known number of days, and worker B is described as being 60 percent more efficient. The question asks how long B would take to do the same job alone, using this efficiency relationship.

Given Data / Assumptions:

• A alone finishes the work in 12 days.
• B is 60% more efficient than A.
• Efficiency means work done per day.
• Both A and B work at constant rates throughout.
• The total work is taken as one complete job.

Concept / Approach:
If a person is 60% more efficient than another, that means the person does 1.60 times as much work per day as the other. Time and efficiency are inversely related: time = work / rate. Therefore, if rate increases by 60%, the time decreases by the same factor, namely 1 / 1.6. We will first compute A's rate, then B's rate, and finally B's time using these relationships.

Step-by-Step Solution:
Total work is assumed to be 1 unit.A's time = 12 days, so A's rate = 1 / 12 work per day.B is 60% more efficient, so B's rate = 1.60 * (1 / 12) = 1.6 / 12.Simplify B's rate: 1.6 / 12 = 16 / 120 = 2 / 15 work per day.Time taken by B alone = 1 / (2 / 15) = 15 / 2 = 7.5 days.

Verification / Alternative check:
Another way is to use proportional reasoning directly. If A takes 12 days, and B is 1.6 times as fast, then B's time is A's time divided by 1.6. So B's time = 12 / 1.6 = 7.5 days. This is exactly the same as the rate based computation, confirming the reliability of the answer.

Why Other Options Are Wrong:
Eight days corresponds to using a factor of 1.5 instead of 1.6, which does not match 60% more efficiency. Six point four days represents dividing by a larger factor than 1.6 and does not respect the given percentage. Five days is even faster and would require an efficiency much greater than 60% more than A. Only 7.5 days is consistent with a 60% increase in efficiency over A's performance.

Common Pitfalls:
Many learners treat 60% more efficient as meaning that B takes 60% of A's time, which would correspond to a 40% reduction in time, not a 60% increase in rate. The correct interpretation is that the rate increases by 60%, while time is inversely proportional to this increased rate. Always convert relative efficiency statements into rate multipliers before calculating time.

Final Answer:
B alone will finish the entire work in 7.5 days.