Explanation:

- Consider the work each person can do in a single day:

- A can complete the work in 10 days, hence does 1/10th of the work per day.

- B can complete the work in 12 days, hence does 1/12th of the work per day.

- C can complete the work in 15 days, hence does 1/15th of the work per day.

- On the first day, A and B work together.

- Combined, they complete 1/10 + 1/12 = 11/60 of the work.

- On the second day, B and C work together.

- Combined, they complete 1/12 + 1/15 = 9/60 of the work.

- In two days, A & B and B & C together complete 11/60 + 9/60 = 20/60 = 1/3 of the work.

- Therefore, repeating the two-day cycle, the complete work will be done in another 2 days.

- In 6 days, three such cycles are completed, so they will finish the work.

- ? Answer: Option 3 - 6 days