Six bells commence tolling together and toll at intervals 2,4,6,8,10 and 12…

2023

Six bells commence tolling together and toll at intervals 2,4,6,8,10 and 12 seconds respectively . In 30 minutes how many times they toll together ?

  1. A.

    4

  2. B.

    10

  3. C.

    15

  4. D.

    16

Attempted by 17 students.

Show answer & explanation

Correct answer: D

Answer: 16

Explanation:

  1. Find the least common multiple of the toll intervals: LCM(2, 4, 6, 8, 10, 12) = 120 seconds.

  2. So the bells toll together every 120 seconds, which is 2 minutes.

  3. Convert 30 minutes to seconds: 30 minutes = 1800 seconds. Number of times they toll together in 1800 seconds = floor(1800 / 120) + 1 = 15 + 1 = 16.

Note: Add 1 because the bells start tolling together at time 0 and that initial simultaneous toll must be counted.

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