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    Question

    The speed of a bike increases by 6 km/hr after every 1 hour. If the distance travelled by the bike in 1st hour is 30 km, the find the total distance travelled by the bike in 16 hours.

    A 1250 km Correct Answer Incorrect Answer
    B 1100 km Correct Answer Incorrect Answer
    C 1200 km Correct Answer Incorrect Answer
    D 1000 km Correct Answer Incorrect Answer

    Solution

    Since, the speed of the bike increases by 6 km/hr after every 1 hour, therefore the bike will travel 6 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 30 km Distance travelled by the bike in 2nd hour = 30 + 6 = 36 km Distance travelled by the bike in 3rd hour = 36 + 6 = 42 km This form an AP i.e. 30, 36, 42………distance travelled in 16th hour Therefore, total distance travelled by the bike in 16 hours = sum of the AP Distance travelled in 16 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 16, a = 1st term = 30 and d = common difference = 6 Therefore, distance travelled in 16 hours = (16/2){2 × 30 + (16 – 1) × 6} = (16/2)(60 + 90) = 1200 km

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