Question

Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. How many times will they toll together in the span of one hour (excluding the toll at the start)?

Answer 1

Answer:10 times

Step-by-step explanation:

LCM of 9,6,4,10,8 is 360sec

360/60=6 minutes

Toll in one hour

6×10=60 minutes i.e in one hour 10 times toll together(excluding toll at the start)

Answer 2

10 times will they toll together in the span of one hour.

Step-by-step explanation:

Given : Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively.

To find : How many times will they toll together in the span of one hour (excluding the toll at the start)?

Solution :

The five bells begin to toll together at intervals of 9 seconds 6 seconds 4 seconds 10 seconds and 8 seconds respectively.

If they toll together right now, then they will together again after an interval which is the least common multiple of 9, 6, 4, 10 and 8 seconds.

2 | 4  6  8  9  10

2 | 2  3  4   9  5

2 | 1   3   2  9  5

3 | 1   3   1  9  5

3 | 1   1   1   3  5

5 | 1   1   1    1   5

  | 1   1   1    1   1

$LCM(4,6,8,9,10)=2\times 2\times 2\times 3\times 3\times 5$

$LCM(4,6,8,9,10)=360$

i.e. bell toll together is 360 second.

We know, 1 hour = 3600 second

Within an interval of 3600 seconds, the bells will toll together excluding the toll at the start is given by,

$\frac{3600}{360}=10$

Therefore, 10 times will they toll together in the span of one hour.

#Learn more

Five bells beginning together toll at intervals of 4,5,7,8 and 10s respectively after what interval of time will they toll again together

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