RRB Paramedical Staff Nurse Model Paper 8

Amount with the person $=\mathit{R}\mathit{s}360$
Let the original number of duration of the tour be $\mathit{x}$ days
Daily expenses per day $=\mathit{R}\mathit{s}\frac{360}{\mathit{x}}$
Given that his tour is extended for 4 days
Hence daily expenses per days $=\mathrm{Rs}\frac{360}{\mathit{x}+4}$
Therefore $\frac{360}{\mathit{x}}-\frac{360}{\mathit{x}+4}=3$
$\Rightarrow \frac{360\left(\mathit{x}+4\right)-360\mathit{x}}{\mathit{x}\left(\mathit{x}+4\right)}=3$
$\Rightarrow 1440=3{\mathit{x}}^2+12\mathit{x}$
$\Rightarrow 3{\mathit{x}}^2+12\mathit{x}-1440=0$
$\Rightarrow {\mathit{x}}^2+4\mathit{x}-480=0$
$\Rightarrow {\mathit{x}}^2+24\mathit{x}-20\mathit{x}-480=0$
$\Rightarrow \mathit{x}\left(\mathit{x}+24\right)-20\left(\mathit{x}+24\right)=0$
$\Rightarrow \left(\mathit{x}+24\right)\left(\mathit{x}-20\right)=0$
$\Rightarrow \left(\mathit{x}+24\right)=0$ or $\left(\mathit{x}-20\right)=0$
$\therefore \mathit{x}=-24$ or $\mathit{x}=20$
since $\mathit{x}$ cannot be negative, $\mathit{x}=20$
Hence his original duration of the tour is 20 days.