Five bells begin to toll together at intervals of 9 seconds, 6 seconds

1.	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. 112. 123. 54. 10
Answer» 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.

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. 112. 123. 54. 10

Answer» 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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