Question

Six bells start tolling together and they toll at intervals of 2, 4, 6, 8, 10, 12 sec respectively, find
(i) after how much time will all six of them toll together?
(ii) how many times will they toll together in 30 min?

Answer 1

The time after which all six bells will toll together must be multiple of 2, 4, 6, 8, 10, 12
Therefore required time = LCM of time intervals
= LCM (2, 4, 6, 8, 10, 12) = 120 sec
Therefore after 120 s all six bells will toll together
After each 120 s i.e. 2 min all bell are tolling together
Therefore in 30 min they will toll together $(\frac{30}{2}+1)=16$ times
1 is added as all the bells are tolling together at he start also i.e. 0th second