Let's assume
Number of days needed after 25 days is x days
1200 men have food for 80 days
so, total men-foods is
[tex]=1200\times 80[/tex]
but at the end of day 25, 320 men retire
So, total men-foods in 25 days is
[tex]=1200\times 25[/tex]
total men-foods after 25 days is
[tex]=(1200-320)\times x[/tex]
now, we can equate them
[tex]1200\times 80=1200\times 25+(1200-320)\times x[/tex]
now, we can solve for x
[tex]30000+\left(1200-320\right)x=1200\times \:80[/tex]
[tex]30000+880x=96000[/tex]
[tex]880x=66000[/tex]
[tex]x=75[/tex]
Hence,
Number of days needed after 25 days is 75 days...........Answer
