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      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?
      A 120km/hr, 240km Correct Answer Incorrect Answer
      B 150km/hr, 200km Correct Answer Incorrect Answer
      C 160 km/hr, 240 km Correct Answer Incorrect Answer
      D 100km/hr, 220km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Suppose the distance is x km andย  Speed of the train is y km/hr Thus, we have two relations: x/y = 90/60 x = 3/2 yย  ย  ย  ย  โ€ฆโ€ฆโ€ฆโ€ฆ(i) x/(y-10) = 96/60 x/(y-10) = 8/5ย  ย  ย  โ€ฆโ€ฆโ€ฆโ€ฆ.(ii) From (i) and (ii), 3/2 yย  = 8/5ย  (y โ€“ 10)ย  3/2 yย  - 8/5 y = - 16 (15y -ย  16y)/10 = - 16 (-y)/10= -16ย  y = 160 Therefore, speed = 160 km/hr andย  Distance, x =ย  3/2 y =ย  ย 3/2ร— 160 = 240 kmย  ย  ย 

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