correct answer is: d) 100 soldiers

Explanation

Here, Food provision for 50 days.
Number of soldiers 500.
After 30 days, there will be remaining days =\left(50-30\right)
\rightarrow 20 days.
Food provision will remain the same.
Now,
There is 20 days of food for 500 soldiers
\therefore There is 1 days of food for =\left(500\times20\right) soldiers
\therefore There is 25 days of food for =\large\left(\frac{500\times20}{25}\right) soldiers
\rightarrow 400 soldiers
\therefore\left(500-400\right)=100 soldiers should leave after 30 days.
Ans: 100 soldiers should leave after 30 days so that the remaining food may last for another 25 days for the remaining soldiers.

Another way, Rules of Three Method

Days and Soldiers are Inversely Proportional.
\therefore\;20\;:\;25\;:\;:\;x\;:\;500
\rightarrow\large\frac{20}{25}=\frac{x}{500}
\rightarrow 25x=20\times500
\rightarrow x=\large\frac{20\times500}{25}
\rightarrow x=400 soldiers
\therefore\left(500-400\right)=100 soldiers should leave after 30 days.
Ans: After 30 days 100 soldiers should leave so that the remaining food may last for another 25 days for the remaining soldiers.

An alternative way to phrase this particular math query is possible:

1. If there is enough food provision for 500 soldiers in a fort to last 50 days, how many soldiers should leave after 30 days so that the remaining food lasts another 25 days for the remaining soldiers?
2. How many soldiers should depart after 30 days to ensure that the food supply for 500 soldiers in a fort lasts for an additional 25 days for the remaining soldiers, given that it initially lasts for 50 days?
3. Given that the food provision for 500 soldiers in a fort lasts for 50 days, how many soldiers should leave after 30 days so that the remaining food lasts for another 25 days for the remaining soldiers?
4. If there is enough food for 500 soldiers in a fort to last for 50 days, how many soldiers should depart after 30 days to extend the remaining food supply for an additional 25 days for the remaining soldiers?