Three bells toll at intervals of 9, 12 and 15 minutes respectively. All three begin to toll at 8 a.m. At what time will they first toll together again?

examrobotsa's picture

Submitted by examrobotsa on

Q: 120 (IAS/2003)
Three bells toll at intervals of 9, 12 and 15 minutes respectively. All three begin to toll at 8 a.m. At what time will they first toll together again?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,3,5,1,3,3,1

keywords: 

{'intervals': [0, 0, 1, 0], 'bells': [0, 0, 1, 0], 'minutes': [0, 0, 1, 1], 'time': [2, 6, 15, 23]}

The problem involves finding the least common multiple (LCM) of the given intervals. The LCM of 9, 12, and 15 minutes is 180 minutes or 3 hours.

Option 1: 8.45 am is only 45 minutes after 8 am i.e. it is before first common toll of all three bells.

Option 2: 10.30 am is 2.5 hours (or 150 minutes) after 8 am which is also less than the LCM (180 minutes or 3 hours). Hence, all three bells wouldn`t toll together at this time.

Option 3: 11 am is exactly 3 hours after 8 am. Therefore, all three bells would toll together exactly at this time because 3 hours is the LCM of the specified intervals.

Option 4: 1.30 pm is 5.5 hours after 8 am. This is past the time the bells first toll together.

So, the correct response is Option 3: 11 am.