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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 27 km, the find the total distance travelled by the bike in 11 hours.
    A 517 km Correct Answer Incorrect Answer
    B 507 km Correct Answer Incorrect Answer
    C 527 km Correct Answer Incorrect Answer
    D 537 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 = 27 km Distance travelled by the bike in 2nd hour = 27 + 4 = 31 km Distance travelled by the bike in 3rd hour = 31 + 4 = 35 km This form an AP i.e. 27, 31, 35………distance travelled in 11th hour Therefore, total distance travelled by the bike in 11 hours = sum of the AP Distance travelled in 11 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 11, a = 1st term = 27 and d = common difference = 4 Therefore, distance travelled in 11 hours = (11/2){2 × 27 + (11 – 1) × 4} = (11/2)(54 + 40) = 517 km

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