To find how long it takes Daniel to complete the same work, we need to use the efficiency relationship between Virat and Daniel.

Step 1: Virat's work rate

Virat completes the work in 30 days, so his work rate is: $\text{Virat's work rate} = \frac{1}{30} \text{ work per day}.$

Step 2: Daniel's efficiency

Daniel is 60% more efficient than Virat. So, Daniel's efficiency is: $\text{Daniel's efficiency} = 1 + 0.60 = 1.60 \times \text{Virat's efficiency}.$

Step 3: Daniel's work rate

Daniel's work rate is 1.60 times Virat's work rate: $\text{Daniel's work rate} = 1.60 \times \frac{1}{30} = \frac{1.60}{30} = \frac{8}{150} \text{ work per day}.$

Step 4: Time taken by Daniel to complete the work

Time taken by Daniel to complete the work is the reciprocal of his work rate: $\text{Time taken by Daniel} = \frac{1}{\frac{8}{150}} = \frac{150}{8} = 18.75 \text{ days}.$

Thus, Daniel can complete the work in 18.75 days.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What if Daniel were 50% more efficient than Virat?
2. How would the time change if both worked together on the task?
3. If Virat's time to complete the work changes to 25 days, what is Daniel's new time?
4. How much work can Daniel complete in 10 days?
5. If a third person, Alex, is 20% less efficient than Virat, how long would it take Alex to finish?

Tip: To compare efficiencies, always convert to rates (work per day) to handle calculations smoothly.