Discussion
Three bells toll at interval of 36 seconds, 40 seconds and 48 seconds respectively. They started ringing together at particular time. They next toll together after?
Answer: A
The bells next toll together after 12 minutes.
They ring together again after the least common multiple of their intervals:
\[ \begin{aligned} 36 &= 2^{2} \times 3^{2} \\ 40 &= 2^{3} \times 5 \\ 48 &= 2^{4} \times 3 \\ \text{LCM} &= 2^{4} \times 3^{2} \times 5 = 720 \end{aligned} \]
720 seconds is 12 minutes.
6 minutes (360 s) is a multiple of 36 and 40 but not of 48. 24 minutes is the second time they toll together, not the next, and 18 minutes (1080 s) is not a multiple of 48.
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