Question

If a train runs at 40 kmph, it reaches the destination 15 minutes late. But if the train runs at 50 kmph, it is late by 5 minutes. Find the distance covered by the train.

• A. 50 km
• B. 43 km
• C. 33 km
• D. 30 km

Answer 1

The correct option is C 33 km

Let the distance be $x$ km.
When the train runs at 40 kmph the time taken to reach the destination is $\frac{x}{40}$ hours and when the train runs at 50 kmph speed the time taken to cover the same distance is $\frac{x}{50}$ hours.

According to the given data, the difference between these two times is 10 minutes or $\frac{10}{60}$ hours.

$\Rightarrow \frac{x}{40}-\frac{x}{50}=\frac{10}{60}\Rightarrow \frac{50x-40x}{2000}=\frac{10}{60}\Rightarrow \frac{10x}{2000}=\frac{1}{6}\Rightarrow x=\frac{1}{6}\times \frac{2000}{10}\Rightarrow x=33.3$

Thus, the distance covered by the train approximately is 33 km.