Question

A train travels $300$ km at a uniform speed. If the speed had been $5$ km an hour more, the journey would have taken $2$ hours less. Find the speed of the train.

• A. $15$
• B. $20$
• C. $25$
• D. $30$

Answer 1

Answer: (C)

$25$

Speed of the train $=x$ km /hr
Time taken $=t$ hrs
$xt=300$

$\therefore t=\frac{300}{x}$

Now, $(x+5)(t-2)=300$

$(x+5)(\frac{300}{x}-2)=300$

$(x+5)(300-2x)=300x$

$300x-2x^2+1500-10x=300x$

$x^2+5x-750=0$

$x^2+30x-25x-750=0$

$(x+30)(x-25)=0$

$x=-30,x=25$

Neglect the negative value, hence, $x=25$ km/hr