A runner starts running from a point at 6:00 am with a speed of 8 km/hr. Another racer starts from the same point at 8:30 am in the same direction with a speed of 10 km/hr. At what time of the day (in p.m.) will the second racer will overtake the other runner?

Speed of first runner = 8 km/hr starting at 6:00 am

Speed of second runner = 10 km/hr starting at 8:30 am

=> Distance covered by the first runner till 8:30 am (2.5 hours) = $$8\times2.5=20$$ km

Now, at 8:30 am, the first runner is 20 km ahead of second runner who just started running and since they are running in same direction, => relative speed = 10 - 8 = 2 km/hr

Time taken to overtake the first runner = distance/speed

= $$\frac{20}{2}=10$$ hours

$$\therefore$$ Time of the day when the second racer will overtake the other runner = 8:30 am + 10 hours = 6:30 pm

=> Ans - (C)