Six bells ring at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. Once, when they start ringing simultaneously for the first time, then determine how many times they will ring together in a continuous span of 30 minutes?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16 times
The bells will ring together at intervals equal to the LCM of their ringing times.
Intervals given:
2, 4, 6, 8, 10, 12 seconds
Step 1: Find LCM
LCM(2, 4, 6, 8, 10, 12) = 120 seconds
So, the bells ring together every 120 seconds.
Step 2: Total time
30 minutes = 30 × 60 = 1800 seconds
Number of times they ring together:
$\frac{1800}{120} = 15$
Including the first simultaneous ringing at the start,
$15 + 1 = 16$