Question 65

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

Solution

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They toll together  after every LCM(2,4,6,8,10,12) seconds = 120 seconds

In 30 min, $$\frac{30\cdot60}{120}\ =\ 15$$

15+1 = 16 times  Because the first bell will be at 0000 hours. Then, second bell will be at 0002 hours and so on. Hence, the bell at the 0030 hours will be the 16th bell. 

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