A can do a piece of work in 12 days. B is 60% more efficient than A (i.e., B’s daily work rate is 1.6 times A’s rate). How many days will B alone take to finish the same work?

Introduction / Context:
Efficiency comparisons directly scale time because time = work / rate. If one person is 60% more efficient, their rate is multiplied by 1.6, so their time is divided by 1.6 for the same job.

Given Data / Assumptions:

• A’s time = 12 days ⇒ r(A) = 1/12 per day.
• B is 60% more efficient ⇒ r(B) = 1.6 * r(A).

Concept / Approach:
B’s time = A’s time / 1.6 = 12 / 1.6.

Step-by-Step Solution:
r(A) = 1/12; r(B) = 1.6 * (1/12) = 1/7.5 per day. Therefore, B’s time = 7.5 days = 7 1/2 days.

Verification / Alternative check:
Check: r(B) * 7.5 = (1.6/12) * 7.5 = 1 (complete job). Works out.

Why Other Options Are Wrong:
6, 6 1/4, 8, 7 days do not equal 12 / 1.6 exactly.

Common Pitfalls:
Adding 60% to the time instead of adjusting the rate; confusing “more efficient” with “takes more time.”

Final Answer:
7 1/2