Question

Three clocks are made to toll at intervals of 24, 32 and 36 seconds respectively. Having tolled together at 10 a.m when will they next do so? How many times will the first clock toll before tolling together next?​

Answer 1

When tolled together at 10 a.m three clocks will next do again at 10: 4.8 a.m. 13 times will the first clock toll before tolling together next.

Given that:

At intervals of 24, 32, and 36 seconds, three clocks are made to toll.

To find:

At 10 a.m when will they next tolled next together and the first clock toll how many times before tolling together next needs to be determined.

Solution:

If they tolled together at 10 a.m so need to find out when will the three bells sound simultaneously once more.

Knowing that at an interval of 24, 32, and 36 seconds the three clocks will toll.

So, taking the L.C.M of 24, 32, and 36.

24 = 2×2×2×3

32 = 2×2×2×2×2

36 = 2×2×3×3

L.C.M of (24, 32, 36) = 2×2×2×2×2×3×3 = 32×9 seconds = 288 seconds.

Converting 288 seconds into minutes = ($\frac{240}{60}$+ $\frac{48}{60}$) minutes = (4 + 0.8) minutes = 4.8 minutes.

Therefore, all three clocks will toll together again at 10: 4.8 am.

As the clocks tolled together at 288 seconds and the first clock toll at 24 seconds then the number of times it tolls will be = $\frac{288}{24}$ = 12 times.

So, at the start, the first clock will toll so add 1 with 12 i.e. 12 + 1 = 13 times.

Hence, the first clock will toll 13 times before tolling together next, and also at 10: 4.8 am all three clocks will toll together.

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