Relative efficiency increase: X can complete a work in 16 days. If Y’s efficiency is 60% more than X’s efficiency, in how many days can Y complete the same work?

Introduction / Context:
Efficiency and time are inversely proportional. “60% more efficient” means the rate is multiplied by 1.6. Therefore, the time to complete a fixed job is divided by 1.6. We apply this directly to X’s 16-day benchmark to find Y’s days.

Given Data / Assumptions:

• X’s time = 16 days ⇒ baseline rate r_X.
• Y’s rate = 1.6 * r_X (60% more efficient).
• Job size is the same for both.

Concept / Approach:
T_Y = T_X / 1.6. This follows from time = work / rate, with work held constant and rate scaled by 1.6.

Step-by-Step Solution:
T_Y = 16 / 1.6 = 10 days.

Verification / Alternative check:
If r_X = 1/16 job/day, then r_Y = 1.6/16 = 0.1 job/day ⇒ 1 / 0.1 = 10 days, consistent.

Why Other Options Are Wrong:
12, 25, 30 days do not correspond to a 60% increase in rate over a 16-day baseline.

Common Pitfalls:
Adding 60% to the time instead of the rate, or subtracting 60%—remember the inverse relation between time and efficiency.

Final Answer:
10 days