Question

7 bells commence tolling together at interval of 2, 4, 6, 8, 10, 20, 30 seconds respectively. In 53 minutes, how many times they toll together?

Answer 1

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Answer 2

Answer:

$\red { number of times the bells toll}$ $\red {together\:in \: 53 \: minutes }$

$\green {= 26 \:times }$

Step-by-step explanation:

Given 7 bells commence tolling together at interval of 2, 4, 6, 8, 10, 20, 30 seconds respectively.

Find the LCM of 2,4,6,8,10,20 and 30:

2 | 2,4,6,8,10,20,30

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2 | 1,2 ,3 ,4 , 5 , 10, 15

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5 | 1, 1 , 3 , 2 , 5, 5, 15

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3 |1, 1 , 3 , 2 , 1 , 1, 3

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** 1 , 1 , 1 , 2 , 1 , 1 , 1

LCM = 2 × 2 × 5 × 3 × 2 = 120

Let the number of times the bells toll together = n

$n = \frac{53 \: minutes }{120\:sec}\\=\frac{53 \times 60\:sec }{120\: sec}$

$= 26.5 \\ ≈ 26$

Therefore.,

$\red { number of times the bells toll}$ $\red {together\:in \: 53 \: minutes }$

$\green {= 26 \:times }$

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