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      Question

      A is cycling at an average speed of 10 km/hr such that

      he can reach a certain point at 12 noon. If he cycles at 30 km/hr, then he will reach the destination at 10 a.m. At what speed he should cycle to reach the destination at 11 a.m.
      A 10 km/hr Correct Answer Incorrect Answer
      B 12 km/hr Correct Answer Incorrect Answer
      C 15 km/hr Correct Answer Incorrect Answer
      D 18 km/hr Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the distance to be travelled be ‘x’ km Time taken when speed is 10 km/hr = (x/10) hours Time taken when speed is 30 km/hr = (x/30) hours According to the question, (x/10) – (x/30) = 2 Or, 3x – x = 2 × 30 Or, 2x = 60 Or, x = 30 km Time taken to travel 30 km with speed of 10 km/hr = 30/10 = 3 hours Therefore, he started at 12 – 3 = 9 a.m. Therefore, required speed to reach the destination at 11 a.m. or 2 hours = 30/2 = 15 km/hr

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