Question : six bells commence tolling together at 7:59 am. They toll at intervals of 3, 6, 9,12, and 15 seconds respectively. How many times will they toll together till 8:16 am? (excluding the toll at 7:59 am)
Option 1: 5
Option 2: 6
Option 3: 3
Option 4: 4
Correct Answer: 5
Solution :
Six bells tolling at 7:59 am
Time duration = 8:16 am - 7:59 am = 17 minutes
All five bells toll together after the interval = Least Common Multiple of 3, 6, 9, 12, and 15
= 180 sec
= 3 minutes
Now,
⇒ Number of tolls = $\frac{\text{Total Time Duration}}{\text{Time interval of tolling together}}$ = $\frac{17}{3}$ = 5.66 (5 times)
Hence, the correct answer is 5.
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