Question

4 bells ring at intervals of 30 minutes, 1 hour, 1 hour 30 minutes and 1 hour 45 minutes respectively. All the bells ring simultaneously at 12 noon. They will again ring simultaneously at:
1. 9 a.m.
2. 3 a.m.
3. 6 a.m.
4. 12 a.m.

Answer 1

Correct Answer - Option 1 : 9 a.m.

Given:

the 4 bells ring at 30 min, 1 h, 1 h 30 min and 1 h 45 min.

Concept Used:

LCM

Conversion of time (hour to minutes)

Calculation:

If we convert the time intervals in minutes we get the 4 bells ringing at an interval of 30 min, 60 min, 90 min and 105 min.

Now once they rang at 12:00 noon they will again ring after a time that is equal to the L.C.M of 30, 60, 90 and 105.

LCM(30, 60, 90, 105) = 1260

⇒ L.C.M of the numbers 30, 60, 90 and 105 is 1260.

Hence, they will again ring simultaneously after 1260 minutes that is equivalent to 21 (=1260/60) hours.

∴ Bells will ring simultaneously after 21 hours.

∵ They ring at 12:00 pm. 

Counting 21 hours after 12 noon, so they again ring at 9:00 am

∴ At 9:00 am they will again ring simultaneously.