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Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. Starting together, how many times will the bells toll together in a span of 1 hour?
1. 11
2. 12
3. 5
4. 10

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Correct Answer - Option 1 : 11

Given:

Five bells commence tolling together and toll at intervals of 9, 6, 4, 10 and 8 seconds respectively.

Concept used:

Least common multiplication 

Calculation:

A least common multiple of (9, 6, 4, 10 and 8)

We can write 9 = 32

4 = 22 

6 = 2 × 3

8 = 23 

10 = 2 × 5

A least common multiple of (9, 6, 4, 10 and 8) = 23 × 32 × 5

⇒ 8 × 9 × 5

⇒ 360 sec

Bells ring together after every 360 sec 

Required number of times in 1 hour (60 × 60 seconds) = [(60 × 60)/360]

⇒ 10

But we have to add 1 because at starting all bells will be rung once a time after that the ring 10 times.

⇒ 10 + 1 

⇒ 11 times 

∴ The required number of times when they toll together is 11.

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