Symbiosis National Aptitude Test SNAP 2014 Paper

Let the usual speed of the aeroplane be x km/h.
Then, $\frac{1500}{\mathit{x}}-\frac{1}{2}$ = $\frac{1500}{\left(\mathit{x}+250\right)}$
$\frac{1500}{\mathit{x}}-\frac{1500}{\mathit{x}+250}$ = $\frac{1}{2}$
⇒ $\frac{1500\mathit{x}+3750000-1500\mathit{x}}{\mathit{x}\left(\mathit{x}+250\right)}$ = $\frac{1}{2}$
⇒ 750000 = ${\mathit{x}}^2$ + 250x or ${\mathit{x}}^2$ + 250x – 750000 = 0
⇒ ${\mathit{x}}^2$ + 1000 x – 750 x – 75000 = 0
⇒ (x + 1000) (x – 750) = 0
⇒ x = 750, – 1000
Speed cannot be negative
We get x = 750 km/h