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Question

Five bells begin to toll together and toll respectively at intervals of 6,5,7,10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start.


A

7 times

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B

8 times

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C

9 times

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D

11 times

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Solution

The correct option is B

8 times


Step 1. Find the LCM

To toll together we need to take the LCM of each seconds of bell

Factor of 6 is

6=2×3

Factor of 5 is

5=1×5

Factor of 7 is

7=1×7

Factor of 10 is

10=2×5

Factor of 12 is

12=2×2×3

Therefore the LCM of 6,5,7,10 and 12 is

LCM6,7,5,10,12=420

Step 2. Find the interval of time at which they toll together.

We know that

420seconds=7minutes [1minutes=60seconds]

So the bells will toll together after every 7minutes

We know that

1hour=60minutes

Therefore the bell will toll together 8 times 8×7=56 excluding the one at the start.

Hence the correct option is B.


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