Explanation:

- Initial Work Details: 45 people take 10 days to repair the road, working 6 hours each day.

- Total Work Calculation: Total work is calculated as number of people × number of days × hours per day, which equals 45 × 10 × 6 hours.

- Work by 30 People: If 30 people are completing the same work, they also work 6 hours per day, so we need to find how many days this takes.

- Equation Setup: 45 people × 10 days = 30 people × X days.

- Solve for X: X = (45 × 10) / 30 = 15 days.

- Conclusion: 30 people, working 6 hours a day, will complete the work in 15 days.

- Correct Answer: Option 1, 15 days.