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      Question

      The speed of a bike increases by 5 km/hr after every 1

      hour. If the distance travelled by the bike in 1st hour is 10 km, the find the total distance travelled by the bike in 14 hours.
      A 595 km Correct Answer Incorrect Answer
      B 590 km Correct Answer Incorrect Answer
      C 597 km Correct Answer Incorrect Answer
      D 585 km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Since, the speed of the bike increases by 5 km/hr after every 1 hour, therefore the bike will travel 5 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 10 km Distance travelled by the bike in 2nd hour = 10 + 5 = 15 km Distance travelled by the bike in 3rd hour = 15 + 5 = 20 km This form an AP i.e. 10, 15, 20………distance travelled in 14th hour Therefore, total distance travelled by the bike in 14 hours = sum of the AP Distance travelled in 14 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 14, a = 1st term = 10 and d = common difference = 5 Therefore, distance travelled in 14 hours = (14/2){2 × 10 + (14 – 1) × 5} = (14/2)(20 + 65) = 595 km

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