Management Aptitude Test 2016 Paper

(a) Let initial speed be x km/h.
Then, final speed = (x + 10) km/h
Also, distance = 75 km
According to the question,
$\frac{75}{\mathit{x}}-\frac{75}{\mathit{x}+10}=\frac{1}{4}$
⇒ $\frac{75\left(\mathit{x}+10\right)-75\mathit{x}}{\mathit{x}\left(\mathit{x}+10\right)}=\frac{1}{4}$
⇒ 75x +750 - 75x = $\frac{{\mathit{x}}^2+10\mathit{x}}{4}$
⇒ 750 x 4 = ${\mathit{x}}^2$ + 10 x
⇒ ${\mathit{x}}^2$ + 10x - 3000 = 0
∴ x = $\frac{-10\pm \sqrt{{10}^2+4\times 3000}}{2}$
= $\frac{-10\pm \sqrt{100+12000}}{2}$
= $\frac{-10\pm 110}{2}=\frac{100}{2}$
= 50 km/h
∴ Required time = $\frac{300}{\left(50+10\right)}=\frac{300}{60}$ = 5 h