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    Question

    Four bells start ringing together

    at 9:00 am. They ring at intervals of 15 seconds, 20 seconds, 30 seconds, and 40 seconds. At what time will they ring together again?
    A 9:20 am Correct Answer Incorrect Answer
    B 9:00 am Correct Answer Incorrect Answer
    C 9:02 am Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    All the four bells ring together at 9:00 am, and after that, they ring at different intervals. The time after which they will ring together again is the LCM of [15, 20, 30, 40].

    15 = 3¹ × 5¹ 20 = 2² × 5¹ 30 = 2¹ × 3¹ × 5¹ 40 = 2³ × 5¹

    So, the required LCM = 2³ × 3¹ × 5¹ = 8 × 3 × 5 = 120 seconds = (120/60) = 2 minutes. So, after 2 minutes from 9:00 am, they will ring together again, i.e., at 9:02 am.

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