Question
Download Solution PDFThree 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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