Question

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

Answer 1

Given that $1200$ soldiers in a fort had enough food for $28$ days
Let the number of soldiers transferred to another fort be $x$
After $4$ days, number of soldiers $=(1200–x)$
Given that food lasted for $32$ more days.

There is inverse relation between the number of soldiers and the number of days food will last for them. so the product of no. of days and no. of soldiers will be constant.

Hence $1200\times 24=(1200–x)\times 32$

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

$\Rightarrow (1200–x)=900$

$\Rightarrow x=1200–900=300$
Thus $300$ soldiers were transferred to another fort.