Question

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 kmph. What is the initial speed of the train (in kmph)?

• A. 25

Answer 1

The correct option is A 25
Let the speed of train be $x$ km/hr.
$\text{Distance travelled}=300\text{km}$
$\Rightarrow \text{Time taken, t}=\frac{300}{x}$
If the speed is increased by 5 kmph, then the time taken to complete the same distance is given by
$T=\frac{300}{x+5}.$
From question, we have $t-T=2.$
$\Rightarrow \frac{300}{x}-\frac{300}{x+5}=2$
$\Rightarrow 300(x+5)-300x=2x(x+5)\Rightarrow 2x^2+10x-1500=0\Rightarrow x^2+5x-750=0$
i.e., $x^2+30x-25x-750=0$
$\Rightarrow x(x+30)-25(x+30)=0$
$\Rightarrow (x+30)(x-25)=0$
$\Rightarrow x=-30,25$
Since speed cannot be negative, the initial speed of the train is 25 kmph.