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    Question

    The speed of a bike increases by 3 km/hr after every 1

    hour. If the distance travelled by the bike in 1st hour is 25 km, the find the total distance travelled by the bike in 20 hours.
    A 1070 km Correct Answer Incorrect Answer
    B 1170 km Correct Answer Incorrect Answer
    C 1470 km Correct Answer Incorrect Answer
    D 1970 km Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Since, the speed of the bike increases by 3 km/hr after every 1 hour, therefore the bike will travel 3 km extra after every 1 hour. Therefore, distance travelled by the bike in 1st hour = 25 km Distance travelled by the bike in 2nd hour = 25 + 3 = 28 km Distance travelled by the bike in 3rd hour = 28 + 3 = 31 km This form an AP i.e. 25, 28, 31………distance travelled in 20th hour Therefore, total distance travelled by the bike in 20 hours = sum of the AP Distance travelled in 20 hours = (n/2){2a + (n – 1)d} Where n = number of terms = 20, a = 1st term = 25 and d = common difference = 3 Therefore, distance travelled in 20 hours = (20/2){2 × 25 + (20 – 1) × 3} = (20/2)(50 + 57) = 1070 km

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