Explanation:

- Let initial number of soldiers = x.

- Food for 200 days for x soldiers is the same as food for 1 soldier for 200x days.

- After 20 days, food left = (200-20) = 180 days for x soldiers.

- 100 more soldiers join, so total soldiers = x + 100.

- This food now lasts for 80 days for x + 100 soldiers.

- So, 180x = 80(x + 100).

- Solve: 180x = 80x + 8000 ? 100x = 8000 ? x = 80.

- So, the initial number of soldiers is 80.

- Therefore, the correct answer is:

Option 4: 80