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 more days. How many soldiers left the fort ?

Answer 1

Period = 28 days
After 4 day, the remaining period
= 28 - 4 = 24 days
In the beginning number of soldiers in the fort = 1200 P
eriod for which the food lasted = 32 days
Let for x soldier,.the food was sufficient,
then
$\begin{array}{ccc}\text{Soldiers}& 1200& x\\ \text{Period (in days)}& 24& 32\end{array}$
More days, less soldiers
By inverse variation
$1200:x=32:24\Rightarrow \frac{1200}{x}=\frac{32}{24}\Rightarrow 32x=24\times 1200\Rightarrow x=\frac{24\times 1200}{32}\Rightarrow x=900$
$\therefore$ Soldiers left = 1200-900=300