a) 250 soldiers

b) 200 soldiers

c) 150 soldiers

d) 100 soldiers

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:

**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?****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?****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?****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?**