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.

• A. $300\frac{km}{hr}$
• B. $400\frac{km}{hr}$
• C. $420\frac{km}{hr}$
• D. $320\frac{km}{hr}$

Answer 1

The correct option is A $300\frac{km}{hr}$

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 or 300.
But speed can't be negative.
$\Rightarrow x=300.$

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