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      Question

      While going to a destination after travelling 75km, the

      driver noticed some problem in the clutch of the train due to which he had to proceed at 2/5 of its former rate and reached the destination 5 hours late. Had the problem in the clutch happened 15 km further on, it would have arrived 30 minutes sooner. Find the speed of the train.
      A 60km/hr Correct Answer Incorrect Answer
      B 50km/hr Correct Answer Incorrect Answer
      C 75km/hr Correct Answer Incorrect Answer
      D 100km/hr Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let A is the starting point and B is actual point where train started facing problems C is the assumed point train started facing problems Given BC = 15km and Difference of is 30 minutes basically due to the speed covering this 15km. Let original speed = x km/hr ∴ Speed after clutch problem = 2x/5 km/hr ⇒ 15/(2x/5) - 15/x = 30/60 ⇒ 75/2x - 15/x = 1/2 ⇒ (75 - 30 )/2x = 1/2 ⇒ (45 )/2x = 1/2 ⇒ x = (45 × 2)/2 ∴ x= 45 km/hr

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