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      Question

      The speed of a bike increases by 8 km/hr after every 1

      hour. If the distance travelled by the bike in 1st hour is 12 km, the find the total distance travelled by the bike in 15 hours.
      A 1020 km Correct Answer Incorrect Answer
      B 1000 km Correct Answer Incorrect Answer
      C 1120 km Correct Answer Incorrect Answer
      D 1720 km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Since, the speed of the bike increases by 8 km/hr after every 1 hour, therefore the bike will travel 8 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 12 km Distance travelled by the bike in 2nd hour = 12 + 8 = 20 km Distance travelled by the bike in 3rd hour = 20 + 8 = 28 km This form an AP i.e. 12, 20, 28………distance travelled in 15th hour Therefore, total distance travelled by the bike in 15 hours = sum of the AP Distance travelled in 15 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 15, a = 1st term = 12 and d = common difference = 8 Therefore, distance travelled in 15 hours = (15/2){2 × 12 + (15 – 1) × 8} = (15/2)(24 + 112) = 1020 km

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