Question

$100$ persons had food provision for $24$days. If $20$persons left the place , the provision will last for

• A. $30$ days
• B. $\frac{96}{5}$ days
• C. $120$days
• D. $40$ days.

Answer 1

The correct option is A

$30$ days

Number of persons and number of days for which food available for them is inversely proportional i.e. less people will have the provision of food for more days.

Number of people remaining now = $100-20=80.$

Let the number of days for which the provision of food will last now be $x.$

Number of people	$100$	$80$
Number of days	$24$	$x$

We know that in inverse variation ,

$$\begin{gathered} \Rightarrow 100\times 24=80\times x \\ \Rightarrow x=\frac{100\times 24}{80} \\ \Rightarrow x=\frac{2400}{80} \\ \Rightarrow x=30 \end{gathered}$$

So , the number of days for which the provision of food will last now are $30$ days.