Question

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Brainleist

Answer 1

Solution :-

Given : Five bells begin tolling together and toll at intervals of 2, 6, 8, 10 and 12 seconds respectively.

For finding the time when all the five bells toll together, we have to find its LCM :

By Prime factorisation method :

2 = 2

6 = 2 × 3

8 = 2³

10 = 2 × 5

12 = 2² × 3

LCM of 2, 6, 8, 10 and 12 = 2³ × 3 × 5 = 120

So, All the five bells toll together after every 120 seconds or 2 minutes.

Total number of times all the five bells toll together in 45 minutes = 45/2 = 22½

In 45 minutes it tolls 22 times and at the starting it toll one time. So, (22 + 1) = 23

Answer : All the five bells toll together 23 times in 45 minutes.

Answer 2

Question:

Five bells begin rolling together and roll at intervals of 2, 6, 8, 10 and 12 seconds respectievly. In 45 minute how many time do they roll together.

Solution:

Five bells begin rolling together and roll at intervals of 2, 6, 8, 10 and 12 seconds respectievly.

At first, we have to find the LCM if the given numbers i.e.

• 2 = 2

• 6 = 2 × 3

• 8 = 2 × 2 × 2

• 10 = 2 × 5

• 12 = 2 × 2 × 3

LCM of 2, 6, 8, 10 and 12 is (2)³ × 3 × 5

→ 8 × 15 = 120

All the balls run together after 120 seconds.

=> 120/60 = 2 min.

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Now..

All balls take 120 seconds or 2 min to run together.

In 45 minutes = 45/2

=> 22.5 minutes

=> 23 (approx.)

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In 45 minutes they (ball) roll 23 times all together.

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