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      Question

      The speed of a bike increases by 4 km/hr after every 1

      hour. If the distance travelled by the bike in 1st hour is 20 km, the find the total distance travelled by the bike in 12 hours.
      A 504 km Correct Answer Incorrect Answer
      B 500 km Correct Answer Incorrect Answer
      C 514 km Correct Answer Incorrect Answer
      D 524 km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Since, the speed of the bike increases by 4 km/hr after every 1 hour, therefore the bike will travel 4 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 20 km Distance travelled by the bike in 2nd hour = 20 + 4 = 24 km Distance travelled by the bike in 3rd hour = 24 + 4 = 28 km This form an AP i.e. 20, 24, 28………distance travelled in 12th hour Therefore, total distance travelled by the bike in 12 hours = sum of the AP Distance travelled in 12 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 12, a = 1st term = 20 and d = common difference = 12 Therefore, distance travelled in 12 hours = (12/2){2 × 20 + (12 – 1) × 4} = (12/2)(40 + 44) = 504 km

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