Let [tex]x[/tex] be the amount of food needed for one man for one day. At the beginning, we have enough food for 400 men for 40 days, i.e.
[tex]400\cdot 40\cdot x = 16000x[/tex]
After 10 days, the 400 men will have consumed
[tex]400\cdot 10\cdot x = 4000x[/tex]
food, impliying that the food remaining is
[tex]16000x-4000x=12000x[/tex]
If 200 more men join the garrison, there are now 600 men. Each of them requires [tex]x[/tex] food each day, and there are [tex]12000x[/tex] units of food remaining. They will last
[tex]\dfrac{12000x}{600}=20[/tex] days.
