Question

A train travels at a certain speed for a distance of 105 km and then travels a distance of 120 km at a speed of 6 km/h more than its original speed. If it takes 5 hours to complete the total journey, then the original speed of the train is

• A. 40 km/hr
• B. 42 km/hr
• C. 48 km/hr
• D. 62 km/hr

Answer 1

The correct option is B 42 km/hr

Let the original speed of the train be x km/h.
Time taken by the train, travelling at a speed of x km/h, $\left(t_1\right)=\frac{105}{x}h$
Time taken by the train, travelling at a speed of (x + 6) km/h, $\left(t_2\right)=\frac{120}{x+6}h$
Total time to complete the journey is 5 h.
$\therefore \frac{105}{x}+\frac{120}{x+6}=5$
$\Rightarrow \frac{105(x+6)+120x}{x(x+6)}=5$
$\Rightarrow 105x+630+120x=5x^2+30x$
$\Rightarrow 5x^2-195x-630=0$
$\Rightarrow x^2-39x-126=0$
$\Rightarrow x^2-42x+3x-126=0$
$\Rightarrow x(x-42)+3(x-42)=0$
$\Rightarrow (x+3)(x-42)=0$
$\Rightarrow x=-3orx=42$
Neglecting negative value, we get the original speed of the train to be 42 km/h.
Hence, the correct answer is option (2).