Explanation:

- Combined Work: X and Y together can finish the work in 10 days. Therefore, their combined daily work rate is 1/10 of the work per day.

- Efficiency Comparison: X is 40% more efficient than Y. If Y’s efficiency is ‘E’, then X’s efficiency is 1.4E. Combined, they do 1.4E + E = 2.4E of work daily.

- Individual Contribution: Let Y’s work rate be ‘E’. So, E + 1.4E = 2.4E = 1/10, solving gives E = 1/24. Y will take 24 days for the work alone, X will take approximately 17.14 days.

- X’s Task: X completes 35% of the work in (35/100) × 17.14 ˜ 6 days.

- Options: The options are checked for the correct time in days for X to complete 35% of work.

- Correct Option: Option 1 - 6 days