Question

An aeroplane takes 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr than its usual speed. Find its usual speed in km/hr.

• A. 300

Answer 1

The correct option is A 300
Let the usual speed of the plane be $x\frac{km}{hr}.$

As per the question,

$\left[\frac{1200}{x}\right]-\left[\frac{1200}{(x+100)}\right]=1$

$\Rightarrow 1200(x+100)-1200x=x(x+100)$
$\Rightarrow 120000=x^2+100x$
$\Rightarrow x^2+100x-120000=0$
$\Rightarrow x^2+400x-300x-120000-0$
$\Rightarrow (x+400)(x-300)=0$

Thus, $x=-400\text{or}300$.
But speed can't be negative.
$\Rightarrow x=300.$

Thus, the usual speed of the place is 300 $\frac{km}{hr}.$