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 for an extra 32 days. How many soldiers left the fort?

Answer 1

We are given that in a fort, 1200 soldiers had enough food for 28 days.
Let x soldiers left after 4 days, thus, remaining soldiers = 1200 - x
Now, for these remaining soldiers food lasts for 32 days.
As number of soldiers decrease, food lasts long.

Thus, situation after 4 days is
$$\begin{gathered} 1200\times 24=\left(1200-x\right)\times 32 \\ \Rightarrow \left(1200-x\right)=\frac{1200\times 24}{32} \\ \Rightarrow 1200-x=900 \\ \Rightarrow x=1200-900 \\ \Rightarrow x=300 \end{gathered}$$

Thus, 300 soldiers left the fort after 4 days.