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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 20 km, the find the total distance travelled by the bike in 14 hours.
    A 715 km Correct Answer Incorrect Answer
    B 725 km Correct Answer Incorrect Answer
    C 735 km Correct Answer Incorrect Answer
    D 705 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 = 20 km Distance travelled by the bike in 2nd hour = 20 + 5 = 25 km Distance travelled by the bike in 3rd hour = 25 + 5 = 30 km This form an AP i.e. 20, 25, 30………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 = 20 and d = common difference = 14 Therefore, distance travelled in 14 hours = (14/2){2 × 20 + (14 – 1) × 5} = (14/2)(40 + 65) = 735 km

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