Three bells commence tolling together and toll at intervals of 8 sec, 10 sec and 12 sec respectively. In 30 min, how many times do they toll together?

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SSC GD Constable (2022) Official Paper (Held On : 31 Jan 2023 Shift 1)
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  1. 14
  2. 17
  3. 16
  4. 18

Answer (Detailed Solution Below)

Option 3 : 16
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Detailed Solution

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Given:

Bells toll at intervals of 8 sec, 10 sec, and 12 sec

Total time = 30 min = 1800 sec

Concept:

The time when all the bells toll together is the least common multiple (LCM) of the tolling intervals.

Solution:

⇒ LCM of 8, 10, and 12 = 120 sec

⇒ Number of times the bells toll together = Total time / Time when all the bells toll together = 1800/120 = 15 times

However, it is important to note that the bells tolled together at the start of the period under consideration.

Therefore, we need to add 1 to the 15 times they toll together within 30 minutes.

So, in total, the bells toll together 15 + 1 = 16 times in 30 minutes.

Therefore, in 30 minutes, the bells toll together 16 times.

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