Question

It takes one and a half hour less to cover a journey of 450 km if the speed of a bus is increased by 10 km/hr. The original speed of the bus is ___ km/hr.

• A. 52
• B. 45
• C. 55
• D. 50

Answer 1

The correct option is D

50

Let speed of the bus be x km/hr
With speed x, time taken= $\frac{450}{x}$
With increased speed, i.e. x + 10, time taken = $\frac{450}{x+10}$
According to the question
$\frac{450}{x}-\frac{450}{x+10}=\frac{3}{2}$
$450(x+10)-450x=\frac{3x(x+10)}{2}$
$150(x+10-x)=\frac{x^2+10x}{2}$
$3000=x^2+10x$
$x^2+10x-3000=0$
Solving which, we get
x = 50 or x = -60
Taking only positive value for speed, x = 50 km/hr