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

Hint: For this question , we have to apply the concept of direct proportion after that suppose the unknown number or value then represent all values in a box then calculate it as we calculate the one variable equation.

Complete step-by-step answer:
It is given that $1200$soldiers are present in the fort and they had enough food with them for 28days
After 4days some soldiers left the fort.
Let us suppose the number of soldiers that left the fort was $x$.
After 4 days the fort had enough food for $1200$ soldiers for $28-4=24\,days$
Now we will represent all data in a table

Number of soldiers	$1200$	$1200-x$
Number of days for which food lasts	$24$	$32$

Here one relation between number of days and number of soldiers is inversely proportion which means , when the number of soldiers the food would last for more days.
$1200\times 24=\left( 1200-x \right)\times 32$
$\Rightarrow$ $\dfrac{1200\times 24}{32}=1200-x$
$\Rightarrow$ $900=1200-x$
$\Rightarrow$ x=1200-900
$\Rightarrow$ x =300
Hence, $300$ soldiers were left in the fort.
Additional information: Inverse proportion- inverse proportion occurs when one value increases and the correlated values decreases.
For example: As speed goes up, automatically travel time will go down.

Note: Sometimes students are unable to differentiate between direct or inverse proportion. In case of direct proportion when one value increases or decreases , the related value also increases or decreases.
For example: If we buy more items , it will cost more money.