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?
Solution:
It is given that after 4 days, out of 28 days, the fort had enough food for 1200 soldiers for $(28-4=24)$ days.
Let $x$ be the number of soldiers who left the fort.
Since the number of soldiers and the number of days for which the food lasts are in inverse variation, we have :
$1200 \times 24=(1200-x) \times 32$
$\Rightarrow \frac{1200 \times 24}{32}=1200-x$
$\Rightarrow 900=1200-x$
$\Rightarrow x=1200-900$
$=300$
Thus, 300 soldiers left the fort.