Priya can complete a piece of work in 16 days. Sai is 60 percent more efficient than Priya. In how many days will Sai alone complete the same work?

Introduction / Context:
This question is a straightforward application of the relationship between efficiency and time. When a worker is more efficient, they can complete the same work in proportionally less time. The key here is to interpret “60 percent more efficient” correctly and then adjust the time needed for Sai using this efficiency factor.

Given Data / Assumptions:

• Priya completes the work in 16 days.
• Sai is 60 percent more efficient than Priya.
• Both workers are assumed to have constant efficiency.
• The amount of work is the same in both cases.

Concept / Approach:
Efficiency is inversely proportional to time when the amount of work is fixed. If Sai is 60 percent more efficient than Priya, then Sai's efficiency is multiplied by a factor of 1.6 relative to Priya. Therefore, Sai's time will be Priya's time divided by 1.6. This proportional reasoning is much quicker than setting up detailed equations, though you can also use a rate and work approach if you prefer.

Step-by-Step Solution:
Let the total work be W units. Priya does W units in 16 days ⇒ Priya's daily work rate = W / 16. Sai is 60 percent more efficient ⇒ Sai's efficiency = 1.6 times Priya's. So Sai's daily work rate = 1.6 * (W / 16) = (1.6W) / 16. Simplify: 1.6 / 16 = 0.1 ⇒ Sai's rate = 0.1W per day = W / 10. Time taken by Sai alone = Total work / Sai's rate = W / (W / 10) = 10 days.

Verification / Alternative check:
Instead of using W, think in terms of ratios. Let Priya's efficiency be 1 unit. Then Sai's efficiency is 1 + 0.6 = 1.6 units. Time is inversely proportional to efficiency, so Sai's time : Priya's time = 1 : 1.6. Therefore Sai's time = 16 / 1.6 = 10 days, which matches the earlier calculation.

Why Other Options Are Wrong:
If Sai took 8 days, he would be exactly twice as efficient as Priya, that is 100 percent more efficient, not 60 percent. 12 or 14 days would mean his efficiency increase is far less than 60 percent. Only 10 days is consistent with the specified increase of 60 percent in efficiency.

Common Pitfalls:
A typical error is to treat 60 percent more efficient as meaning that Sai's time is 60 percent of Priya's time, which would give 16 * 0.6 = 9.6 days and then rounded incorrectly. The correct way is to scale efficiency, not time, and then use the inverse relationship between time and efficiency.

Final Answer:
Sai alone will finish the work in 10 days.