Question

$1200$ men can finish a stock of food in $35$ days. How many more men should join them so that the same stock may last for $25$ days $?$

Answer 1

Step: Calculate the extra men required

Given: $1200$ men can finish a stock of food in $35$ days

Let the number of men required to finish the stock of food in $25$ days be $‘x^{\prime }$

Number of men	$1200$	$x$
Number of days	$35$	$25$

Clearly, more men will consume the food in less number of days and less number of men will consume the food in more number of days. It is, therefore, the case of inverse variation.
$\Rightarrow \text{Ratio of number of men}=\text{Inverse ratio of number of days}$

$\Rightarrow \frac{1200}{x}=\frac{25}{35}$
$\Rightarrow x=48\times 35$
$\Rightarrow x=1680$
$\Rightarrow \text{Extra men}=1680–1200=480$

Hence, $480$ extra men are required to finish the same stock of food in $25$ days.