Question
A train covers a distance between stations Dehradun to
Rudrapur in 90minutes. If the speed is reduced by 10 km/hr, it will cover the same distance in 96 minutes. What is the distance between the two stations (in km)? Also find the speed of train?Solution
Suppose the distance is x km and Speed of the train is y km/hr Thus, we have two relations: x/y = 90/60 x = 3/2 y    …………(i) x/(y-10) = 96/60 x/(y-10) = 8/5   ………….(ii) From (i) and (ii), 3/2 y = 8/5 (y – 10) 3/2 y - 8/5 y = - 16 (15y - 16y)/10 = - 16 (-y)/10= -16 y = 160 Therefore, speed = 160 km/hr and Distance, x = 3/2 y =  3/2× 160 = 240 km  Â
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