Question

A train leaves the station $1$ hour before the scheduled time. The driver decreases its speed by $50$ km/hr. At the next station $300$ km away the train reached on time. Find the original speed of the train.

• A. $100$ km/hr
• B. $150$ km/hr
• C. $125$ km/hr
• D. $200$ km/hr

Answer 1

Answer: (B)

$150$ km/hr

Let the normal speed of the train $=x$ km/hr.

Then the normal time to cover $300$ km $=\frac{300}{x}$.

Now it takes $1$ hour more.

So, the new time taken $=$ $1+\frac{300}{x}=\frac{x+300}{x}$.

$\therefore$ the new speed $=300÷\frac{x+300}{x}$ km/hr

$=$ $\frac{300x}{x+300}$ km/hr..

But the new speed is $(x=50)$ km/hr.

$\Rightarrow \frac{300x}{x+300}=x-50$

$\Rightarrow x^2-50x-15000=0$

$\Rightarrow (x-150)(x+100)=0$

$\Rightarrow x=(150,-100)$ km/hr.

We reject the negative value as the train always runs in the same direction.

$\therefore x=150$

So, the normal speed of the train $=150$ km/hr.

Ans- Option B.