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?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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