Explanation:

- T alone completes the work in 12 days.

* This means T's work rate is 1/12 of the work per day.

- T and U completed one-third of the work in 3 days.

* Combined, their work rate for 3 days was 1/3 of the work.

* So, their combined daily work rate is (1/3) / 3 = 1/9 of the work.

- Finding U's work rate.

* T's work rate is 1/12.

* Combined rate of T and U is 1/9.

* U's work rate = (Combined rate) - (T's rate) = 1/9 - 1/12.

* U's work rate = 4/36 - 3/36 = 1/36 of the work per day.

- U can complete the work alone in 36 days.

* U's daily work rate implies full work in 36 days.

- Correct Answer: Option 1 - 36 days