Question

A train running between two stations $A$ and $B$ arrives at its destination $10$ minutes late when its speed is $50$ km/hr and $50$ minutes late when its speed is $30$ km/hr. How far is station $A$ from $B$?

• A. $50$ km
• B. $20$ km
  
• C. $60$ km
  
• D. $15$ km
  

Answer 1

The correct option is A $50$ km

Let the distance between A and B is x km

Then time taken with speed 50 km\h =$\frac{x}{50}$ hr

AND time taken with speed 30 km\h =$\frac{x}{30}$ hr

But time deference In both Speed $i=50-10=40$ sec

$\therefore \frac{x}{50}-\frac{x}{30}=\frac{10}{60}-\frac{50}{60}\Rightarrow \frac{20x}{1500}=\frac{2}{3}\Rightarrow 60x=3000\Rightarrow x=50$ m

Distence A and B is $50$ km