Six bells commence tolling together and toll at the intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

Six bells commence tolling together and toll at the intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? Correct Answer 16 times

Given:

Total time = 30 min.

Intervals of 2, 4, 6, 8, 10 and 12 seconds

Calculation:

LCM of 2, 4, 6, 8, 10 and 12 

2 = 2

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

10 = 2 × 5

12 = 2 × 2 × 3

LCM of 2, 4, 6, 8, 10 and 12 = 2³ × 3 × 5 = 120 sec. = 2 min

Number times do they toll together = (30/2) + 1 = 16

∴ Required answer is option 4.

Mistake Point: At zero second ring will ring for 1st time. So, we have to add 1.