Question

there are 4 bells which toll at intervals of 3; 7 ;12 and 14 seconds respectively. the four Bells begin to toll at 12 o'clock. when will the next toll together and how often they do so in 14 minutes

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

(i.) Therefore the 4 bells ring together at 12:01:24.

(ii.) Therefore all bells toll together 10 times in 14 minutes.

Given:

4 bells toll at intervals of 3, 7, 12, and 14 seconds.

The 4 bells begin to toll at 12 'o clock.

To Find:

(i.) The 4 bells toll together at what time?

(ii.) How many times do 4 bells toll together in 14 minutes?

Solution:

The given question can be solved as shown below.

(i.) The LCM of the interval of all 4 bells gives the time after which they toll again together.

LCM of 3, 7, 12, and 14:

2 I 3, 7, 12, 14

3 I 3, 7, 6, 7

7 I 1, 7, 2, 7

2 I 1, 1, 2, 1

    1, 1, 1, 1

Hence the LCM of 3, 7, 12, and 14 = 2 × 3 × 7 × 2 = 84

So, the 4 bells ring together after 84 seconds after 12'o clock and the time is 12 hours 1 min, and 24 seconds.

Therefore the 4 bells ring together at 12:01:24.

(ii.) Number of seconds present in 14 minutes = 14 × 60 = 840 seconds

⇒ The number of times the 4 bells ring together in 14 minutes = ( Total Time )/( Time interval taken for 4 bells to ring together )
⇒ The number of times the 4 bells ring together in 14 minutes = 840/84 = 10 times.

Therefore all bells toll together 10 times in 14 minutes.

(i.) Therefore the 4 bells ring together at 12:01:24.

(ii.) Therefore all bells toll together 10 times in 14 minutes.

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