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?

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 31 Jan 2023 Shift 1)

Answer 1

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.