Question

If a train travelled 5 km/hr slower, it would take one hour more to travel 210 km. The speed of the train is :

• A. 30 km/hr
• B. 35 km/hr
• C. 70 km/hr
• D. 60 km/hr

Answer 1

The correct option is B

35 km/hr

Let the speed of the train be x km/hr.
Distance travelled = 210 km

Time taken to travel 210 km = $\frac{210}{x}$ hours

When the speed is decreased by 5 km/h, the new speed is (x-5)

Time taken to travel 210 km with the new speed is $\frac{210}{x-5}$ hours

According to the question,
$\frac{210}{x-5}-\frac{210}{x}=1$
$\Rightarrow 210x-210(x-5)=x(x-5)$
$\Rightarrow 210x+1050-210x=x^2-5x$
$\Rightarrow x^2-5x-1050=0$
$\Rightarrow (x-35)(x+30)=0$
$\Rightarrow x=35,-30$

The speed cannot be negative. Thus, the speed of the train is 35 km/hr