Question

If a train travels at a speed of 50 kmph, it reaches its destination 10 minutes late. But if it travels at a speed of 60 kmph, it reaches its destination 5 minutes earlier. Find the distance covered to reach its destination.

• A. 100 km
• B. 75 km
• C. 95 km
• D. 85 km

Answer 1

The correct option is B 75 km

Let the distance covered be $xkm$.

If the speed of the train is 50 kmph, time taken to reach the destination is $\frac{x}{50}$ hr.

If the speed of the train is 60 kmph, time taken to reach the destination is $\frac{x}{50}$ hr.

According to the available data, the difference between these two times is 15 minutes or $\frac{15}{60}$ hr.

Therefore,
$\Rightarrow \frac{x}{50}-\frac{x}{60}=\frac{15}{60}\Rightarrow \frac{6x-5x}{300}=\frac{1}{4}\Rightarrow \frac{x}{300}=\frac{1}{4}\Rightarrow x=\frac{300}{4}\Rightarrow x=75$

Thus, the distance covered to reach its destination is 75 km.