Question

$1200$ soldiers in a fort had enough food for $28days$. After $4days$, some soldiers were sent to another fort and thus the food lasted for $32$ more days. How many soldiers left the fort?

Answer 1

Had the soldiers would not have left, the food lasted for remaining days would be

$=1200\times (28-4)$

$=1200\times 24$ units

Let the number of soldiers left be $x$

Therefore, number of soldiers left are $1200-x$

Since, food lasted for them for $32$ days, therefore, amount of food available for them is

$=(1200-x)\times 32$

Since, amount of food remains constant, therefore,

$\Rightarrow 1200\times 24=(1200-x)\times 32$

$\Rightarrow \frac{1200\times 24}{32}=1200-x$

$\Rightarrow 300\times 3=1200-x$

$\Rightarrow x=1200-900=300$

Thus, $300$ soldiers left the fort.