Question 14 Marks
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
View full question & answer→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:
$1200\times24=(1200-\text{x})\times32$
$\Rightarrow(1200-\text{x})=\frac{1200\times24}{32}$
$\Rightarrow1200-\text{x}=900$
$\text{x}=1200-900$
$\Rightarrow\text{x}=300$
Thus, 300 soldiers left the fort after 4 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:
$1200\times24=(1200-\text{x})\times32$
$\Rightarrow(1200-\text{x})=\frac{1200\times24}{32}$
$\Rightarrow1200-\text{x}=900$
$\text{x}=1200-900$
$\Rightarrow\text{x}=300$
Thus, 300 soldiers left the fort after 4 days.