Explanation:

- A's Work Rate: A completes half the work in 36 days, so A can do the full work in 72 days.

- B's Work Rate: There seems to be an incomplete or typo statement about B's contribution; assuming it should say, "B does 1/3 of the work in 12 days," meaning B can complete the full work in 36 days.

- Together with C: A, B, and C together complete the work in 24 days.

- Combined Rate of A+B+C: Their combined daily work rate is 1/24 of the work per day. A's rate is 1/72, B's rate is 1/36.

Using the formula:

$$

\frac{1}{72} + \frac{1}{36} + \frac{1}{C} = \frac{1}{24}

$$

- Solve for C

$$

\frac{1}{72} + \frac{1}{36} = \frac{1}{24} - \frac{1}{C}

$$

$$

= \frac{2}{72} + \frac{1}{72} = \frac{1}{72}

$$

$$

= \frac{1}{24} - \frac{3}{72} = \frac{1}{C}

$$

Simplifying further:

$$

\frac{1}{C} = \frac{1}{24} - \frac{1}{24}

$$

$$

\frac{1}{C} = \frac{1}{144}

$$

- C works alone 144 days to complete the work.

- Correct Option: Option 4 - 144 days