Question

An aeroplane departed 30 minutes later than its scheduled time and in order to reach its destination which is 1500 km away on time, it had to increase its speed by 250 km/hr. Its original speed is ___ km/hr.

• A. 750
• B. 700
• C. 800
• D. 725

Answer 1

The correct option is A

750

Let the original speed of the plane be $x$ km/hr. Then,

Time taken to cover 1500 km with the original speed $=\frac{1500}{x}hrs$

Time taken to cover 1500 m with the speed of $(x+250)km/hr=\frac{1500}{x+250}$

$\therefore \frac{1500}{x}=\frac{1500}{x+250}+\frac{1}{2}$

$\Rightarrow \frac{1500}{x}-\frac{1500}{x+250}=\frac{1}{2}$

$\Rightarrow \frac{1500x+1500\times 250-1500x}{x(x+250)}=\frac{1}{2}$

$\Rightarrow \frac{1500\times 250}{x^2+250x}=\frac{1}{2}$

$\Rightarrow 750000=x^2+250x$

$\Rightarrow x^2+250x-750000=0$

$\Rightarrow x^2+1000x-750x-750000=0$

$\Rightarrow x(x+1000)(x-750)=0$

$\Rightarrow x=-1000or,x=750\Rightarrow x=750$ [$\therefore$ speed cannot be negative]

Hence, the original speed of the plane is 750 km/hr