Explanation:

- Determine individual work rates:

- Sanju completes the work in 12 days, so his work rate is \( \frac{1}{12} \) work/day.

- Suraj completes the work in 16 days, so his work rate is \( \frac{1}{16} \) work/day.

- Sanjay completes the work in 24 days, so his work rate is \( \frac{1}{24} \) work/day.

- Combine their work rates:

- Combined rate = \( \frac{1}{12} + \frac{1}{16} + \frac{1}{24} \).

- Calculate the combined rate:

- Find a common denominator (48) and add:

$$ \frac{4}{48} + \frac{3}{48} + \frac{2}{48} = \frac{9}{48} = \frac{3}{16} $$.

- Find the total time together:

- Total time = \( \frac{1}{\frac{3}{16}} = \frac{16}{3} \) days.

- Correct Option:

- Option:1, \( \frac{16}{3} \) days