Question

An express train takes $30$ min less for a journey of $440$ km, if its usual speed is increased by $8$ km/hr. Find its usual speed(in km/hr).

• A. $80$
• B. $45$
• C. $65$
• D. $8$

Answer 1

The correct option is A $80$

Let the speed of the car be $s$ and time be $t$
Then, $st=440⟹s=\frac{440}{t}$
and $(s+8)(t-\frac{1}{2})=440$
$(\frac{440}{t}+8)(2t-1)=880$
$(8t+440)(2t-1)=880t$
$16t^2-8t+880t-440=880t$
$16t^2-8t-440=0$
$2t^2-t-55=0$
$2t^2-11t+10t-55=0$
$(2t-11)(t+5)=0$
$t=5.5,-5$
Hence time is $5.5$ hr
Speed $=\frac{440}{5.5}=80km/hr$