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    Question

    Amit has two routes, ‘X’ and

    ‘Y’, to travel from his home to his gym. The length of route ‘X’ exceeds the length of route ‘Y’ by 15 km. On Monday, Amit chose route ‘X’. He traveled at a certain speed for 2 hours, then increased his speed by 20% for the rest of the journey. On Tuesday, he opted for route ‘Y’. For the first 2 hours, he traveled at a speed that was 20% less than his initial speed on Monday, and then increased his speed by 25% for the remainder of the journey. If Amit completed both routes in exactly 3 hours, determine the distance of the longer route.
    A 45 km Correct Answer Incorrect Answer
    B 75 km Correct Answer Incorrect Answer
    C 80 km Correct Answer Incorrect Answer
    D 65 km Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    For route ‘X’: Let the speed of Amit for 2 hours be ‘a’ km/hr Therefore, total distance covered = 2a + 1.2a = 3.2a km For route ‘Y’: Speed of Amit for 2 hours = 0.8a km/hr Therefore, total distance covered = 0.8a × 2 + 1.25 × 0.8a = 2.6a km According to the question, 3.2a – 2.6a = 15 Or, a = 15/0.6 = 25 Therefore, distance of the longer route = 3.2a = 80 km

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