Question 15 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.