Question

$4$ Bells toll together at $9:00\mathrm{A}.\mathrm{M}.$ They toll after $7,8,11$ and $12$ $\mathrm{seconds}$ respectively. How many times will they toll together again in the next $3$ hour?

Answer 1

To find the time at which all bells will toll together, we have to find the L.C.M of the given numbers.

So, L.C.M of $7,8,11\&12=$$1848$

$\Rightarrow$bells will toll together after every $1848\mathrm{seconds}$ or $\frac{1848}{60}=30.80\approx 31\mathrm{minutes}$.

In three hours, no.of seconds $=30\times 3600=108,000\mathrm{seconds}$

In three times or three hours, bells will toll $=\frac{108000}{1848}=5\mathrm{times}$.

So, the sequence in which bells will toll together after $9:00\mathrm{A}.\mathrm{M}$ in next three hours will be

$9:00\mathrm{A}.\mathrm{M},9:31\mathrm{A}.\mathrm{M},10:02\mathrm{A}.\mathrm{M},10:33\mathrm{A}.\mathrm{M},11:04\mathrm{A}.\mathrm{M}\&11:35\mathrm{A}.\mathrm{M}$