Question 995562

a garrison of 600 men had provision for 25 days.after 9 days an addition of men was made and the remaining provision latest only for 4 days.find the number added.
<pre>{{{M = k(c)/T}}}, with:
M being number of men

k being constant of variation

c being consumption

T being time
{{{600 = k(1)/25}}}
{{{600 = k/25}}}
{{{k = 600(25)}}}, or 15,000



In 9 days, we get:
{{{M = k(c)/T}}}
{{{600 = 15000(c)/9}}}
{{{600 = 15000c/9}}}
{{{15000c = 600(9)}}}
c, or fraction consumed in 9 days = {{{600(9)/15000}}}, or {{{9/25 }}}


In 9 days, {{{9/25}}} of the provision was consumed by 600 men, so {{{1 - 9/25}}}, or {{{16/25}}} of provision remain

With additional men being A, we get:
{{{M + A = k(c)/T}}}
{{{600 + A = 15000(16/25)/4}}}
{{{600 + A = 600(16)/4}}}
600 + A = 2,400

A, or additional men = 2,400 - 600, or {{{highlight_green(1800)}}}</pre>