A train running between two stations A and B arrives at its destination 10 minutes late when its speed is 50 km/h and 50 minutes late when its speed is 30 km/h. What is the distance between the stations A and B ?

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70 km

60 km

50 km

40 km

answer is B.

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Detailed Solution

Let the distance between the two stations be $x km$ .

Then,

$\frac{x}{50} - \frac{10}{6} = \frac{x}{30} - \frac{50}{6} \Rightarrow \frac{x}{50} - \frac{1}{6} = \frac{x}{30} - \frac{5}{6}$

Or $\frac{x}{30} - \frac{x}{50}$ $= \frac{2}{3}$

Or $x = 50 km$

Thus distance between the station A and B $= 50 km$

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