Explanation:

- Aman and Deep complete the work in 1/3rd of the time Jay takes.

- Deep and Jay complete it in 1/5th of the time Aman takes.

- Together, Aman, Deep, and Jay can finish in 20 days.

- Assigning variables:

- Let $A$ be the time Aman takes alone.

- Let $D$ be the time Deep takes alone.

- Let $J$ be the time Jay takes alone.

- Given equations:

- $\frac{1}{A}+\frac{1}{D}=\frac{3}{J}$

- $\frac{1}{D}+\frac{1}{J}=\frac{5}{A}$

- $\frac{1}{A}+\frac{1}{D}+\frac{1}{J}=\frac{1}{20}$

- Solving these gives $A=120$.

- Option 3: 120 days is the correct answer.