Question

Three bells toll together at 9am. They toll after 3,5 and 8 seconds respectively. How many times tolling sound will appear in one hour? Assume only one tolling sound when one or more than one bells toll together

Answer 1

Your Answer:

Given:-

Three bells toll after every 3,5 and 8 seconds respectively.

To find:-

How many times it will toll in 1 hours.

Solution:-

First finding the LCM of 3,5 and 8

We get LCM(3,5,8)=120sec.

So we have to find how many time bell toll in 120sec.

First the smallest number, that is 3secs

120/3= 40times.

Then in the 5sec

120/5= 24times

Then in the 8sec

120/8 = 15times

So total = 40+24+15 = 79times.

LCM of 3 and 5 = 15.

Every interval of 15sec must be reduced as it is repeated in 3sec and 5sec tolling.

120/15= 8times

LCM of 3 and 8 = 24

Every interval of 24sec must be reduced as it is repeated in 3sec and 8sec tolling.

120/24=5times

LCM of 8 and 5 = 40

Every interval of 40 sec must be reduced as it is repeated in 5sec and 8sec tolling.

120/40=3times.

And to add 1 time of tolling extra as 120 is reduced from every tolling.

So total in 120sec or 2min

= 79-(8+5+3)+1

= 80-16

= 64

So, in 1 hour = (60÷2) × 64

= 30 × 64

= 1920 times.

So total tolling is 1920 times without any repetition.