Question

In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel. How long will these provisions last ?

Answer 1

Number of girls in the beginning a 50
More girls joined a 30
$\therefore$ Total number of girls = 50 + 30 a 80
Let the provisions last for x days. Then
$\begin{array}{ccc}\text{Girls}& 50& 80\\ \text{Period (in days)}& 40& x\end{array}$
More girls, less days
$\therefore$ By inverse variation
$50:80=x:40\Rightarrow \frac{50}{80}=\frac{x}{40}\Rightarrow 50\times 40=80\times x\Rightarrow x=\frac{50\times 40}{80}\Rightarrow x=25$
$\therefore$ The provisions were last for = 25 days