Correct Answer - Option 1 : 16
Given:
Six bells start tolling together and toll at intervals of 2, 4, 6, 8 10 seconds respectively.
Concept:
LCM = Least Common Multiple
Calculation:
LCM can be found out by prime factorization
2 = 1 × 2
4 = 22
6 = 2 × 3
8 = 23
10 = 2 × 5
LCM (2, 4, 6, 8, 10) = 23 × 3 × 5 = 120
Bells toll together after every 120 seconds.
Number of tolling the bells in 30 minutes = (30 minutes × 60 seconds)/120
⇒ 1800 seconds/ 120 = 15
∴ Total number of times of the tolling of bells after they toll for the first time
⇒ 15 + 1 = 16
If two bells after 2 seconds and 5 seconds respectively and they start tolling at the same time.
Then, the first bell tolls after every 2, 4, 6 secs.....
⇒ The second bell tolls after every 5, 10, 15 secs
So, they toll together again after 10 seconds, which is the LCM.
∴ They toll after 10 seconds, that is whenever the time is a common multiple of 2 and 5 both.
Since the bells start tolling together, the first toll also needs to be counted, that is the number of times of tolling since the first time.
