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?
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? Correct Answer 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) =
⇒ 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.
