Question

A bus takes 5 hours more than a train to cover the distance of 900 km from Vardha to Pune. lf speed of the train is 15 km/hr more than that of the bus, then what is the speed of bus per hour?

• A. 60 km/hr
• B. 75 km/hr
• C. 55 km/hr
• D. 45 km/hr

Answer 1

The correct option is D 45 km/hr

Let speed of bus = $x$ km/hr
Let time taken by train = t hr
Distance travelled by bus = Speed of bus x time taken by bus .....(1)
$900=x(t+5)$
Distance travelled by train = Speed of train time taken by train ....(2)
$900=(x+15)t$
From eqs. (1) and (2)
$x(t+5)=(x+15)t$
$xt+5x=xt+15t$
$\Rightarrow x=3t$
Putting this in eq. (1)
$900=3t(t+5)$
$\Rightarrow 3t^2+15t-900=0\Rightarrow t^2+5t-300=0$
$(t+20)(t-15)=0,t=-20,l=15$
'$t$' can not be negative $\therefore t=15$
$900=\left(x\right)(15+5)$

$\Rightarrow x=\frac{900}{20}=45km/hr$