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A gym has 6 different bells for 6 different exercises which ring at the end of each exercise. The duration of the exercises are 40, 45, 50, 60, 75 and 125 seconds. If the bells ring together at 9 AM, then at what time next will they ring together?

A gym has 6 different bells for 6 different exercises which ring at the end of each exercise. The duration of the exercises are 40, 45, 50, 60, 75 and 125 seconds. If the bells ring together at 9 AM, then at what time next will they ring together? Correct Answer 11:30 AM

Given:

4 Bells ring after 40, 45, 50, 60, 75 and 125 seconds respectively

Concept used:

The lowest common multiple (LCM) concept is used because LCM would give us the time interval at which the four bells ring simultaneously.

Calculations:

According to the question, we have

40 = 2 × 2 × 2 × 5 

45 = 3 × 3 × 5 

50 = 2 × 5 × 5 

60 = 2 × 2 × 3 × 5 

75 = 3 × 5 × 5 

125 = 5 × 5 × 5 

⇒ LCM of (40, 45, 50, 60, 75,125) = 5 × 5 × 3 × 2 × 2 × 2 × 3 × 5

⇒ 9000

LCM of (40, 45, 50, 60, 75,125) = 9000

Thus, all bells ring after 9000 seconds = 9000/3600 hour

⇒ 5/2 hour

⇒ 2 hour 30 min

The time they ring together again = 9 am + 2h 30 min

⇒ 11:30 AM

∴ At 11:30 AM they will ring together again.

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