If a man runs at 6 kmph from his house, he misses the train at the station by 8 min. If he runs at 10 kmph, he reaches 7 min before the departure of the train. What is the distance of the station from his house? (in Km).

Solution (By Examveda Team)

Let the distance of the station from the house of the person = x km
$$\eqalign{ & {\text{Difference}}\,{\text{of}}\,{\text{time}} \cr & = 8 + 7 \cr & = 15\,{\text{minutes}} \cr & = \frac{1}{4}\,hr \cr & {\text{Since}},\, \cr & {\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}} \cr & \therefore \frac{x}{6} - \frac{x}{{10}} = \frac{1}{4} \cr & \Rightarrow \frac{{10x - 6x}}{{60}} = \frac{1}{4} \cr & \Rightarrow \frac{{2x}}{{30}} = \frac{1}{4} \cr & \Rightarrow x = \frac{{15}}{4} = 3\frac{3}{4}km \cr} $$