Explanation:

- Initially, the food is meant for a certain number of soldiers for 200 days.

- After 20 days, the food quantity remains for 180 days.

- Let's denote the initial number of soldiers as X.

- The food consumed by X soldiers in 180 days is the same as food for (X + 100) soldiers in 80 days.

- We set up an equation based on this: $(X\times 180)=((X+100)\times 80)$.

- Solving this equation, $180X=80X+8000$.

- Simplifying gives $100X=8000$.

- Therefore, $X=80$.

Based on this reasoning, the correct answer is:

Option:4, 80